1. Meaning of Square Root
The square root of a non-negative number N is the non-negative number whose square is equal to N.
Key Rule:
If a2 = N and a ≥ 0, then:
√N = a
Examples:
√25 = 5 because 52 = 25.
√144 = 12 because 122 = 144.
√625 = 25 because 252 = 625.
Terminology:
The symbol √ is called the radical sign. The number written inside the radical sign is called the radicand.
2. Principal Square Root
Important Convention:
The symbol √N denotes the principal or non-negative square root of N.
Therefore:
√49 = 7
Important Difference:
√49 = 7, but the equation x2 = 49 has two real solutions:
x = 7 and x = −7
Common Mistake:
Do not write √49 = ±7. The symbol √49 represents only the principal square root 7.
3. Important Square Roots to Remember
Common Values:
√1 = 1
√4 = 2
√9 = 3
√16 = 4
√25 = 5
√36 = 6
√49 = 7
√64 = 8
√81 = 9
√100 = 10
√121 = 11
√144 = 12
√169 = 13
√196 = 14
√225 = 15
√256 = 16
√289 = 17
√324 = 18
√361 = 19
√400 = 20
√441 = 21
√484 = 22
√529 = 23
√576 = 24
√625 = 25
√676 = 26
√729 = 27
√784 = 28
√841 = 29
√900 = 30
Exam Strategy:
Memorising squares and square roots at least up to 30 saves considerable time in simplification, approximation, algebra and quantitative aptitude questions.
4. Square Root by Prime Factorisation
The prime-factorisation method is especially useful when the given number is a perfect-square integer.
Method:
1. Express the number as a product of prime factors.
2. Group identical prime factors into pairs.
3. Take one factor from each pair.
4. Multiply the selected factors.
Example:
Find √1764.
1764 = 22 × 32 × 72
Therefore:
√1764 = 2 × 3 × 7
= 42
Shortcut:
If:
N = p2aq2br2c,
then:
√N = paqbrc
5. Why Prime Factors Are Taken in Pairs
Reason:
Every prime factor of a perfect square occurs an even number of times.
Example:
144 = 24 × 32
√144
= 22 × 3
= 4 × 3
= 12
Observation:
Taking the square root of a perfect square halves each even prime exponent.
6. Square Root of a Fraction
Rule:
For a ≥ 0 and b > 0:
√(a/b) = √a / √b
Example:
√(49/121)
= √49 / √121
= 7/11
Example:
√(225/400)
= 15/20
= 3/4
Shortcut:
If possible, simplify the fraction before taking its square root.
7. Square Root of a Mixed Fraction
Method:
Convert the mixed fraction into an improper fraction first. Then take the square root of its numerator and denominator.
Example:
Find √(2 14/25).
2 14/25 = 64/25
√(64/25)
= 8/5
= 1 3/5
Common Mistake:
Do not take the square root of the whole-number part and fractional part separately.
8. Square Root of a Decimal
A terminating decimal may be converted into a fraction and then its square root can be evaluated.
Example:
√0.81
= √(81/100)
= 9/10
= 0.9
Example:
√0.0081
= √(81/10000)
= 9/100
= 0.09
Exam Tip:
Remember common decimal squares such as:
0.12 = 0.01
0.22 = 0.04
0.32 = 0.09
0.42 = 0.16
0.52 = 0.25
0.62 = 0.36
0.72 = 0.49
0.82 = 0.64
0.92 = 0.81
9. Decimal Places in Perfect Decimal Squares
Useful Rule:
When a terminating decimal is an exact square of another terminating decimal, its decimal places may be grouped in pairs from the decimal point.
The square root contains one decimal place for every pair of decimal places in the perfect-square decimal.
Example:
√2.25 = 1.5
2.25 has 2 decimal places and its square root has 1 decimal place.
Example:
√0.0009 = 0.03
0.0009 has 4 decimal places and its square root has 2 decimal places.
Important:
An even number of decimal places alone does not prove that a decimal is a perfect square.
10. Square Root by Long Division Method
The long-division method is useful for large perfect squares as well as for obtaining decimal approximations of non-perfect squares.
Main Steps:
1. Starting from the decimal point, group the digits into pairs.
2. Find the largest perfect square not exceeding the first group.
3. Write its square root as the first digit of the root.
4. Subtract its square and bring down the next pair.
5. Double the root obtained so far.
6. Find a suitable next digit to complete the new divisor.
7. Multiply and subtract.
8. Continue the process as required.
11. Long Division Example — √2025
Example:
Find √2025.
Group the digits:
20 | 25
Largest perfect square not exceeding 20:
42 = 16
First digit of the root = 4.
20 − 16 = 4.
Bring down the next pair 25:
425.
Double the current root 4:
2 × 4 = 8.
Now choose the digit 5 because:
85 × 5 = 425.
Therefore:
√2025 = 45
Verification:
452 = 2025.
12. Pairing Digits in Long Division
Pairing Rule:
Starting from the decimal point:
• Group digits in pairs towards the left.
• Group digits in pairs towards the right.
• If necessary, append zeros on the right side of the decimal.
Example:
For 182.25, the grouping is:
1 | 82 . 25
Observation:
√182.25 = 13.5 because:
13.52 = 182.25.
13. Finding Decimal Square Roots by Long Division
Rule:
Once the integer part has been exhausted, place the decimal point in the root and continue bringing down pairs of zeros when additional decimal places are required.
Example:
For a non-perfect square such as √2, long division can be continued by writing:
2.000000...
and bringing down pairs of zeros to obtain successive decimal digits.
Exam Tip:
Do not continue unnecessary decimal calculation if the question only asks for the nearest integer or an interval.
14. Estimating a Non-Perfect Square Root
Basic Method:
Find the two consecutive perfect squares between which the number lies.
Example:
Estimate √70.
82 = 64
92 = 81
Since:
64 < 70 < 81,
8 < √70 < 9
Exam Tip:
This simple comparison is often enough to eliminate three options immediately.
15. Integer Part of a Square Root
Rule:
If:
n2 < N < (n+1)2,
then the integer part of √N is n.
Example:
Find the integer part of √150.
122 = 144
132 = 169
Therefore:
12 < √150 < 13
Integer part = 12.
16. Nearest-Integer Estimation
Method:
Compare the given number with the squares of nearby integers.
Example:
Which integer is √80 closest to?
82 = 64
92 = 81
80 is much closer to 81 than to 64.
Therefore √80 is closest to 9.
17. Quick Approximation Near a Perfect Square
Approximation Formula:
If N is close to a2, then:
√N ≈ a + (N − a2)/(2a)
Example:
Approximate √102.
100 = 102
√102
≈ 10 + (102−100)/(2×10)
= 10 + 2/20
= 10.1
Exam Note:
This is an approximation. It should not be presented as the exact square root.
18. Square Root of a Product
Property:
For a ≥ 0 and b ≥ 0:
√(ab) = √a × √b
Example:
√(36 × 25)
= √36 × √25
= 6 × 5
= 30
Shortcut:
When factors inside a square root are perfect squares, separate them before multiplying large numbers.
19. Square Root of a Quotient
Property:
For a ≥ 0 and b > 0:
√(a/b) = √a / √b
Example:
√(324/81)
= 18/9
= 2
20. Square Root of a Square
Fundamental Property:
For any real number a:
√(a2) = |a|
Examples:
√(72) = 7
√((-7)2) = 7
Common Mistake:
For a general real number a, do not write √(a2) = a. The correct result is |a|.
21. Square Root Does Not Distribute over Addition or Subtraction
Incorrect Rule:
√(a+b) = √a + √b
is generally false.
Example:
√(9+16)
= √25
= 5
But:
√9 + √16
= 3+4
= 7
Similarly:
√(a−b) is generally not equal to √a−√b.
22. Scaling Square Roots by Powers of 10
Rules:
√(100N) = 10√N
√(10000N) = 100√N
√(N/100) = √N/10
√(N/10000) = √N/100
Example:
If √2.25 = 1.5, then:
√225
= √(100×2.25)
= 10×1.5
= 15
Decimal Shortcut:
Moving the decimal point by 2 places inside a square root changes the decimal position by 1 place in the square root.
A movement of 4 places inside gives 2 places outside, and a movement of 6 places inside gives 3 places outside.
23. Verification of a Square Root
Fast Verification:
Square the proposed answer.
If x is claimed to be √N, verify whether:
x2 = N
Example:
Check whether √2304 = 48.
482
= (50−2)2
= 2500−200+4
= 2304
Therefore the answer is correct.
24. Common Exam Traps
Trap 1:
Writing √49 = ±7. The correct value is 7.
Trap 2:
Using √(a+b) = √a+√b.
Trap 3:
Writing √(a2) = a for every real a instead of |a|.
Trap 4:
Taking separate square roots of the whole and fractional parts of a mixed fraction.
Trap 5:
Pairing digits incorrectly in the long-division method.
Trap 6:
Moving the decimal point by the same number of places inside and outside the square root.
Trap 7:
Treating an approximate square root as an exact value.
Trap 8:
Forgetting to simplify a fraction when simplification makes its square root obvious.
25. Quick Revision
Remember:
• √N denotes the principal non-negative square root of N.
• √49 = 7, while x2 = 49 gives x = ±7.
• Prime-factorisation method groups equal prime factors in pairs.
• Taking a square root halves even prime exponents.
• √(a/b) = √a/√b for a ≥ 0 and b > 0.
• Convert a mixed fraction into an improper fraction first.
• Terminating decimal perfect squares may be converted into fractions.
• In long division, digits are grouped in pairs from the decimal point.
• If n2 < N < (n+1)2, then n < √N < n+1.
• √(a2) = |a| for real a.
• √(ab) = √a×√b for non-negative a and b.
• √(a+b) is generally not equal to √a+√b.
• A 2-place decimal shift inside the radical produces a 1-place shift in the root.
• Square the proposed answer for quick verification.
26. Verified Previous-Year Questions
RRB NTPC PYQ
Decimal Square Root
4 March 2021 · CBT-I · Shift 1
Q1. Find the square root of 182.25.
A. 11.25
B. 13.5
C. 12.5
D. 9.25
Correct Answer: B. 13.5
13.52 = 182.25.
Therefore:
√182.25 = 13.5.
RRB NTPC PYQ
Mixed Fraction Square Root
16 February 2021 · CBT-I · Shift 1
Q2. Find the square root of 1 11/25.
A. 1 2/5
B. 1 1/5
C. 1 3/5
D. 2 1/5
Correct Answer: B. 1 1/5
1 11/25 = 36/25.
√(36/25)
= 6/5
= 1 1/5.
RRB NTPC PYQ
Decimal Square Root
14 August 2025 · UG CBT-I · Shift 1
Q3. Evaluate √1.0201.
A. 1.02
B. 10.1
C. 101
D. 1.01
Correct Answer: D. 1.01
1.0201 = 10201/10000.
√10201 = 101 and √10000 = 100.
Therefore:
√1.0201 = 1.01.
SSC GD PYQ
Square Root Scaling
9 May 2026 · Shift 3
Q4. If √210.25 = 14.5, find √0.00021025.
A. 1.45
B. 0.145
C. 0.0145
D. 0.00145
Correct Answer: C. 0.0145
0.00021025 = 210.25/106.
Therefore:
√0.00021025
= 14.5/103
= 0.0145.
27. Practice MCQs
Practice MCQ
Q1. Find √2304.
A. 46
B. 47
C. 48
D. 49
Correct Answer: C. 48
482 = 2304. Therefore √2304 = 48.
Practice MCQ
Q2. Find √1764.
A. 38
B. 40
C. 42
D. 44
Correct Answer: C. 42
1764 = 22×32×72. Therefore √1764 = 2×3×7 = 42.
Practice MCQ
Q3. Find √0.0081.
A. 0.009
B. 0.09
C. 0.9
D. 9
Correct Answer: B. 0.09
0.092 = 0.0081.
Practice MCQ
Q4. Find √(2 14/25).
A. 1 1/5
B. 1 2/5
C. 1 3/5
D. 1 4/5
Correct Answer: C. 1 3/5
2 14/25 = 64/25. Thus √(64/25) = 8/5 = 1 3/5.
Practice MCQ
Q5. Find √(49/121).
A. 5/11
B. 6/11
C. 7/11
D. 9/11
Correct Answer: C. 7/11
√49/√121 = 7/11.
Practice MCQ
Q6. Between which consecutive integers does √70 lie?
A. 6 and 7
B. 7 and 8
C. 8 and 9
D. 9 and 10
Correct Answer: C. 8 and 9
64 < 70 < 81. Therefore 8 < √70 < 9.
Practice MCQ
Q7. Find √5625.
A. 65
B. 70
C. 75
D. 85
Correct Answer: C. 75
752 = 5625.
Practice MCQ
Q8. If √x = 13.5, find x.
A. 162.25
B. 172.25
C. 182.25
D. 192.25
Correct Answer: C. 182.25
x = (13.5)2 = 182.25.
Practice MCQ
Q9. Find √0.0009.
A. 0.003
B. 0.03
C. 0.3
D. 3
Correct Answer: B. 0.03
0.032 = 0.0009.
Practice MCQ
Q10. Find √(2025/81).
A. 3
B. 4
C. 5
D. 6
Correct Answer: C. 5
√2025/√81 = 45/9 = 5.
1. Square Root अर्थात वर्गमूल
किसी non-negative number N का square root वह non-negative number है जिसका square N के बराबर होता है।
Key Rule:
यदि a2 = N और a ≥ 0, तो:
√N = a
उदाहरण:
√25 = 5 क्योंकि 52 = 25।
√144 = 12 क्योंकि 122 = 144।
√625 = 25 क्योंकि 252 = 625।
Terminology:
√ को radical sign कहा जाता है। Radical sign के अंदर लिखे number को radicand कहा जाता है।
2. Principal Square Root
महत्वपूर्ण नियम:
√N, N के principal अर्थात non-negative square root को दर्शाता है।
इसलिए:
√49 = 7
महत्वपूर्ण अंतर:
√49 = 7 होता है, लेकिन equation x2 = 49 के दो real solutions हैं:
x = 7 और x = −7
Common Mistake:
√49 = ±7 न लिखें। √49 का value केवल 7 है।
3. Important Square Roots to Remember
Common Values:
√1 = 1, √4 = 2, √9 = 3, √16 = 4, √25 = 5
√36 = 6, √49 = 7, √64 = 8, √81 = 9, √100 = 10
√121 = 11, √144 = 12, √169 = 13, √196 = 14, √225 = 15
√256 = 16, √289 = 17, √324 = 18, √361 = 19, √400 = 20
√441 = 21, √484 = 22, √529 = 23, √576 = 24, √625 = 25
√676 = 26, √729 = 27, √784 = 28, √841 = 29, √900 = 30
Exam Strategy:
कम-से-कम 1 से 30 तक squares एवं square roots याद रखना simplification, approximation, algebra और aptitude questions में calculation speed बढ़ाता है।
4. Prime Factorisation Method से Square Root
Method:
1. Number का prime factorisation करें।
2. समान prime factors के pairs बनाएँ।
3. प्रत्येक pair से एक factor लें।
4. चुने गए factors को multiply करें।
उदाहरण:
√1764 ज्ञात करें।
1764 = 22 × 32 × 72
इसलिए:
√1764 = 2 × 3 × 7
= 42
Shortcut:
यदि:
N = p2aq2br2c,
तो:
√N = paqbrc
5. Prime Factors के Pairs क्यों बनाए जाते हैं?
Reason:
Perfect square में प्रत्येक prime factor की exponent even होती है।
उदाहरण:
144 = 24 × 32
√144
= 22 × 3
= 4 × 3
= 12
Observation:
Perfect square का square root लेने पर उसकी even prime exponents आधी हो जाती हैं।
6. Fraction का Square Root
Rule:
a ≥ 0 तथा b > 0 के लिए:
√(a/b) = √a / √b
उदाहरण:
√(49/121)
= √49/√121
= 7/11
उदाहरण:
√(225/400)
= 15/20
= 3/4
Shortcut:
यदि fraction simplify करने पर calculation आसान होती है, तो पहले fraction को lowest form में reduce करें।
7. Mixed Fraction का Square Root
Method:
Mixed fraction को पहले improper fraction में बदलें। इसके बाद numerator एवं denominator का square root लें।
उदाहरण:
√(2 14/25) ज्ञात करें।
2 14/25 = 64/25
√(64/25)
= 8/5
= 1 3/5
Common Mistake:
Mixed fraction के whole-number part और fractional part का square root अलग-अलग न निकालें।
8. Decimal का Square Root
उदाहरण:
√0.81
= √(81/100)
= 9/10
= 0.9
उदाहरण:
√0.0081
= √(81/10000)
= 9/100
= 0.09
Exam Tip:
Common decimal squares याद रखें:
0.12 = 0.01
0.22 = 0.04
0.32 = 0.09
0.42 = 0.16
0.52 = 0.25
0.62 = 0.36
0.72 = 0.49
0.82 = 0.64
0.92 = 0.81
9. Decimal Places एवं Perfect Decimal Squares
Useful Rule:
यदि terminating decimal किसी terminating decimal का exact square है, तो decimal point से digits को pairs में group किया जा सकता है।
Perfect-square decimal के प्रत्येक दो decimal places के लिए square root में एक decimal place होगा।
उदाहरण:
√2.25 = 1.5
उदाहरण:
√0.0009 = 0.03
Important:
केवल even number of decimal places होना किसी decimal को perfect square prove नहीं करता।
10. Long Division Method से Square Root
Main Steps:
1. Decimal point से digits के pairs बनाएँ।
2. First group से कम या बराबर largest perfect square चुनें।
3. उसका square root root का पहला digit होगा।
4. उसका square subtract करें और next pair नीचे लाएँ।
5. अब तक प्राप्त root को double करें।
6. नया suitable digit चुनें।
7. Multiply करके subtract करें।
8. इसी process को आवश्यकता अनुसार continue करें।
11. Long Division Example — √2025
उदाहरण:
√2025 ज्ञात करें।
Digits के pairs:
20 | 25
20 से कम या बराबर largest square:
42 = 16
Root का first digit = 4।
20 − 16 = 4।
Next pair 25 नीचे लाएँ:
425।
Current root 4 को double करें:
2 × 4 = 8।
अब digit 5 लें क्योंकि:
85 × 5 = 425।
इसलिए:
√2025 = 45
Verification:
452 = 2025।
12. Long Division में Digits की Pairing
Pairing Rule:
Decimal point से शुरू करके:
• Left side में दो-दो digits के groups बनाएँ।
• Right side में भी दो-दो digits के groups बनाएँ।
• आवश्यकता होने पर right side में zeros append करें।
उदाहरण:
182.25 की grouping होगी:
1 | 82 . 25
Observation:
√182.25 = 13.5 क्योंकि:
13.52 = 182.25।
13. Long Division से Decimal Approximation
Rule:
Integer part complete होने के बाद root में decimal point रखें और additional decimal digits प्राप्त करने के लिए radicand में pairs of zeros नीचे लाते रहें।
उदाहरण:
√2 जैसे non-perfect square के लिए number को:
2.000000...
लिखकर pairs of zeros नीचे लाते हुए decimal approximation प्राप्त की जा सकती है।
Exam Tip:
यदि question केवल nearest integer या interval पूछता है, तो unnecessary decimal calculation न करें।
14. Non-Perfect Square Root का Estimation
Basic Method:
Given number के दोनों ओर nearest consecutive perfect squares identify करें।
उदाहरण:
√70 के लिए:
82 = 64
92 = 81
64 < 70 < 81
इसलिए:
8 < √70 < 9
Exam Tip:
Option-based questions में कई बार केवल यह interval identify करना ही पर्याप्त होता है।
15. Square Root का Integer Part
Rule:
यदि:
n2 < N < (n+1)2,
तो √N का integer part n होगा।
उदाहरण:
√150 के लिए:
122 = 144
132 = 169
12 < √150 < 13
इसलिए integer part = 12।
16. Nearest Integer Estimation
उदाहरण:
√80 किस integer के सबसे नजदीक है?
82 = 64
92 = 81
80, 81 के बहुत अधिक close है।
इसलिए √80 का nearest integer 9 है।
17. Nearby Perfect Square से Quick Approximation
Approximation Formula:
यदि N, a2 के बहुत पास है, तो:
√N ≈ a + (N−a2)/(2a)
उदाहरण:
√102 का approximate value निकालें।
100 = 102
√102
≈ 10 + (102−100)/(2×10)
= 10 + 2/20
= 10.1
Exam Note:
यह approximate value है, exact square root नहीं।
18. Product का Square Root
Property:
a ≥ 0 तथा b ≥ 0 के लिए:
√(ab) = √a × √b
उदाहरण:
√(36×25)
= √36 × √25
= 6 × 5
= 30
Shortcut:
यदि radical के अंदर factors perfect squares हैं, तो large multiplication करने से पहले उन्हें separate करना आसान होता है।
19. Quotient का Square Root
Property:
a ≥ 0 तथा b > 0 के लिए:
√(a/b) = √a/√b
उदाहरण:
√(324/81)
= 18/9
= 2
20. Square का Square Root
Fundamental Property:
किसी भी real number a के लिए:
√(a2) = |a|
उदाहरण:
√(72) = 7
√((-7)2) = 7
Common Mistake:
General real a के लिए √(a2) = a न लिखें। सही result |a| है।
21. Addition एवं Subtraction पर Square Root का गलत प्रयोग
गलत Rule:
√(a+b) = √a + √b
सामान्यतः गलत है।
उदाहरण:
√(9+16)
= √25
= 5
लेकिन:
√9 + √16
= 3+4
= 7
इसी प्रकार:
√(a−b) भी सामान्यतः √a−√b के बराबर नहीं होता।
22. Powers of 10 के साथ Square Root Scaling
Rules:
√(100N) = 10√N
√(10000N) = 100√N
√(N/100) = √N/10
√(N/10000) = √N/100
उदाहरण:
यदि √2.25 = 1.5, तो:
√225
= √(100×2.25)
= 10×1.5
= 15
Decimal Shortcut:
Square root के अंदर decimal point को 2 places move करने पर root में decimal position 1 place move करती है।
4 places inside → 2 places outside
6 places inside → 3 places outside
23. Square Root Answer की Verification
Fast Verification:
Proposed answer का square करें।
यदि x को √N बताया गया है, तो check करें:
x2 = N
उदाहरण:
√2304 = 48 को verify करें।
482
= (50−2)2
= 2500−200+4
= 2304
इसलिए answer सही है।
24. Common Exam Traps
Trap 1:
√49 को ±7 लिखना। सही value 7 है।
Trap 2:
√(a+b) = √a+√b मान लेना।
Trap 3:
हर real a के लिए √(a2) = a लिखना। सही form |a| है।
Trap 4:
Mixed fraction के whole एवं fractional parts के square roots अलग-अलग निकालना।
Trap 5:
Long division में digits के pairs गलत बनाना।
Trap 6:
Square root के अंदर एवं बाहर decimal को same number of places shift करना।
Trap 7:
Approximate square root को exact value मान लेना।
Trap 8:
Fraction simplify करने से आसान square root मिलने के बावजूद उसे simplify न करना।
25. Quick Revision
एक नज़र में:
• √N, N का principal non-negative square root है।
• √49 = 7, जबकि x2 = 49 में x = ±7।
• Prime-factorisation method में identical prime factors के pairs बनाए जाते हैं।
• Perfect square का square root लेने पर even prime exponents आधी हो जाती हैं।
• √(a/b) = √a/√b, जहाँ a ≥ 0 और b > 0।
• Mixed fraction को पहले improper fraction में बदलें।
• Decimal perfect squares को fraction form में बदलकर solve किया जा सकता है।
• Long division में digits के pairs decimal point से बनाए जाते हैं।
• यदि n2 < N < (n+1)2, तो n < √N < n+1।
• √(a2) = |a|।
• √(ab) = √a×√b, जहाँ a,b ≥ 0।
• √(a+b) सामान्यतः √a+√b के बराबर नहीं होता।
• Radical के अंदर 2-place decimal shift root में 1-place shift देता है।
• Answer verify करने के लिए उसका square करें।
26. Verified Previous-Year Questions
RRB NTPC PYQ
Decimal Square Root
4 मार्च 2021 · CBT-I · Shift 1
प्रश्न 1. 182.25 का square root ज्ञात करें।
A. 11.25
B. 13.5
C. 12.5
D. 9.25
सही उत्तर: B. 13.5
13.52 = 182.25।
इसलिए:
√182.25 = 13.5।
RRB NTPC PYQ
Mixed Fraction Square Root
16 फरवरी 2021 · CBT-I · Shift 1
प्रश्न 2. 1 11/25 का square root ज्ञात करें।
A. 1 2/5
B. 1 1/5
C. 1 3/5
D. 2 1/5
सही उत्तर: B. 1 1/5
1 11/25 = 36/25।
√(36/25)
= 6/5
= 1 1/5।
RRB NTPC PYQ
Decimal Square Root
14 अगस्त 2025 · UG CBT-I · Shift 1
प्रश्न 3. √1.0201 का value ज्ञात करें।
A. 1.02
B. 10.1
C. 101
D. 1.01
सही उत्तर: D. 1.01
1.0201 = 10201/10000।
√10201 = 101 तथा √10000 = 100।
इसलिए:
√1.0201 = 1.01।
SSC GD PYQ
Square Root Scaling
9 मई 2026 · Shift 3
प्रश्न 4. यदि √210.25 = 14.5 है, तो √0.00021025 का value ज्ञात करें।
A. 1.45
B. 0.145
C. 0.0145
D. 0.00145
सही उत्तर: C. 0.0145
0.00021025 = 210.25/106।
इसलिए:
√0.00021025
= 14.5/103
= 0.0145।
27. Practice MCQs
Practice MCQ
प्रश्न 1. √2304 ज्ञात करें।
A. 46
B. 47
C. 48
D. 49
सही उत्तर: C. 48
482 = 2304। इसलिए √2304 = 48।
Practice MCQ
प्रश्न 2. √1764 ज्ञात करें।
A. 38
B. 40
C. 42
D. 44
सही उत्तर: C. 42
1764 = 22×32×72। इसलिए √1764 = 42।
Practice MCQ
प्रश्न 3. √0.0081 ज्ञात करें।
A. 0.009
B. 0.09
C. 0.9
D. 9
सही उत्तर: B. 0.09
0.092 = 0.0081।
Practice MCQ
प्रश्न 4. √(2 14/25) ज्ञात करें।
A. 1 1/5
B. 1 2/5
C. 1 3/5
D. 1 4/5
सही उत्तर: C. 1 3/5
2 14/25 = 64/25। इसका square root = 8/5 = 1 3/5।
Practice MCQ
प्रश्न 5. √(49/121) ज्ञात करें।
A. 5/11
B. 6/11
C. 7/11
D. 9/11
सही उत्तर: C. 7/11
√49/√121 = 7/11।
Practice MCQ
प्रश्न 6. √70 किन दो consecutive integers के बीच है?
A. 6 एवं 7
B. 7 एवं 8
C. 8 एवं 9
D. 9 एवं 10
सही उत्तर: C. 8 एवं 9
64 < 70 < 81। इसलिए 8 < √70 < 9।
Practice MCQ
प्रश्न 7. √5625 ज्ञात करें।
A. 65
B. 70
C. 75
D. 85
सही उत्तर: C. 75
752 = 5625।
Practice MCQ
प्रश्न 8. यदि √x = 13.5 है, तो x का value ज्ञात करें।
A. 162.25
B. 172.25
C. 182.25
D. 192.25
सही उत्तर: C. 182.25
x = (13.5)2 = 182.25।
Practice MCQ
प्रश्न 9. √0.0009 ज्ञात करें।
A. 0.003
B. 0.03
C. 0.3
D. 3
सही उत्तर: B. 0.03
0.032 = 0.0009।
Practice MCQ
प्रश्न 10. √(2025/81) ज्ञात करें।
A. 3
B. 4
C. 5
D. 6
सही उत्तर: C. 5
√2025/√81 = 45/9 = 5।