1. Basic Idea of Perfect-Square Formation
A positive integer becomes a perfect square when every prime factor in its prime factorisation has an even exponent.
Fundamental Rule:
If:
N = paqbrc,
then N is a perfect square only when a, b, c, ... are all even.
Example:
72 = 23 × 32.
Exponent of 2 is odd, so 72 is not a perfect square.
2. Least Number to Multiply to Make a Perfect Square
Method:
1. Find the prime factorisation.
2. Identify primes having odd exponents.
3. Multiply by one suitable factor of each such prime so that every exponent becomes even.
Example:
Find the least number by which 432 must be multiplied to make a perfect square.
432 = 24 × 33
Exponent of 3 is odd.
Multiply by 3:
432 × 3 = 1296 = 362
Required number = 3.
Shortcut:
The least multiplier is the product of the prime factors whose exponents are odd.
3. Least Number to Divide to Make a Perfect Square
Method:
In prime factorisation, remove one factor from each prime whose exponent is odd so that all remaining exponents become even.
Example:
972 = 22 × 35.
Exponent of 3 is odd.
972 ÷ 3 = 324 = 182.
Least divisor = 3.
Exam Trap:
Do not multiply or divide by every prime factor. Only the factors needed to correct odd exponents are required.
4. Least Number to Add to Obtain a Perfect Square
Rule:
If N lies between two consecutive perfect squares:
n2 < N < (n+1)2,
then the least number to be added is:
(n+1)2 − N
Example:
Find the least number to add to 1450.
382 = 1444
392 = 1521
1450 lies between them.
Required addition
= 1521 − 1450
= 71.
5. Least Number to Subtract to Obtain a Perfect Square
Rule:
If:
n2 < N < (n+1)2,
then the least number to be subtracted is:
N − n2
Example:
For 1450:
382 = 1444.
Required subtraction
= 1450 − 1444
= 6.
Fast Strategy:
For addition, move to the next perfect square.
For subtraction, move back to the previous perfect square.
6. Addition vs Subtraction — Which Is Smaller?
Method:
For a number between n2 and (n+1)2, compare:
N − n2
and
(n+1)2 − N.
Example:
For N = 1450:
Subtraction required = 6.
Addition required = 71.
Therefore subtracting 6 is the smaller adjustment.
7. Least Perfect Square Divisible by a Given Number
Method:
1. Prime-factorise the given number.
2. Make every prime exponent even by multiplying by the minimum required factors.
Example:
Find the least perfect square divisible by 360.
360 = 23 × 32 × 5
To make all exponents even, multiply by 2 × 5 = 10.
360 × 10 = 3600 = 602.
Required perfect square = 3600.
8. Least Perfect Square Divisible by Several Numbers
Method:
1. Find the LCM of all the given numbers.
2. Prime-factorise the LCM.
3. Multiply by the minimum factors needed to make every exponent even.
Example:
Find the least perfect square divisible by 18, 24 and 30.
LCM = 360
= 23 × 32 × 5
Multiply by 2 × 5 = 10.
Required number
= 360 × 10
= 3600.
Common Mistake:
The LCM itself need not be a perfect square. After finding the LCM, its prime exponents must still be checked.
9. Perfect-Square Multiplier from Prime Exponents
Fast Rule:
If:
N = 25 × 34 × 53 × 72,
the odd exponents belong to 2 and 5.
Therefore the least multiplier is:
2 × 5 = 10.
Observation:
Only the parity of each exponent matters: even or odd.
10. Perfect-Square Divisor from Prime Exponents
Fast Rule:
For the same number:
N = 25 × 34 × 53 × 72,
divide by 2 × 5 = 10.
The remaining exponents become:
24 × 34 × 52 × 72,
which is a perfect square.
11. Quick Square of a Number Ending in 5
Shortcut:
For a number ending in 5:
1. Remove the final 5.
2. Multiply the remaining number by its next integer.
3. Append 25.
Example:
852:
8 × 9 = 72
Append 25
852 = 7225.
Example:
1152:
11 × 12 = 132
Append 25
1152 = 13225.
12. Squaring Numbers Near 100
Identity:
(100 ± a)2
= 10000 ± 200a + a2
Example:
982
= (100−2)2
= 10000−400+4
= 9604.
Example:
1032
= (100+3)2
= 10000+600+9
= 10609.
13. Squaring Numbers Near Any Convenient Base
Identity:
(a+b)2 = a2 + 2ab + b2
(a−b)2 = a2 − 2ab + b2
Example:
522
= (50+2)2
= 2500+200+4
= 2704.
Exam Strategy:
Choose a nearby number whose square is already easy to calculate.
14. Finding the Next Square from a Known Square
Rule:
(n+1)2 = n2 + 2n + 1
Example:
If 402 = 1600, then:
412
= 1600 + 81
= 1681.
Shortcut:
To move from n2 to the next square, add the next odd number 2n+1.
15. Finding the Previous Square from a Known Square
Rule:
(n−1)2 = n2 − (2n−1)
Example:
If 502 = 2500, then:
492
= 2500−99
= 2401.
16. Fast Square-Root Identification Using Nearby Squares
Method:
When a number is a known perfect square, compare it with nearby memorised squares.
Example:
Find √4489.
602 = 3600
702 = 4900
Try 67:
672
= (60+7)2
= 3600+840+49
= 4489.
Therefore:
√4489 = 67.
17. Using the Unit Digit to Narrow a Square Root
Unit-Digit Pairs:
Square ends in 1 → root may end in 1 or 9.
Square ends in 4 → root may end in 2 or 8.
Square ends in 5 → root ends in 5.
Square ends in 6 → root may end in 4 or 6.
Square ends in 9 → root may end in 3 or 7.
Square ends in 0 → root ends in 0.
Important:
The unit digit narrows the possibilities but usually does not determine the complete square root by itself.
18. Quick Square Root of Four-Digit Perfect Squares
Strategy:
1. Locate the number between two nearby hundreds of squares.
2. Determine the tens digit of the root from the leading digits.
3. Use the unit digit of the square to determine possible unit digits.
4. Test the remaining possibilities.
Example:
Find √7744.
802 = 6400
902 = 8100
So the root is between 80 and 90.
7744 ends in 4, so the root must end in 2 or 8.
Possible roots: 82 or 88.
882 = 7744.
Therefore:
√7744 = 88.
19. Square Roots of Numbers Ending in 25
Observation:
If a perfect square ends in 25, its integer square root ends in 5.
Example:
√5625
The root must end in 5.
Since 702 = 4900 and 802 = 6400, the root lies between 70 and 80.
The only possibility ending in 5 is 75.
Therefore:
√5625 = 75.
20. Choosing the Fastest Method
Exam Strategy:
• Prime exponents visible → use exponent balancing.
• Least addition/subtraction → locate neighbouring perfect squares.
• Several divisibility conditions → first find LCM.
• Number ending in 5 → use the ending-5 squaring shortcut.
• Number near 10, 50, 100, etc. → use algebraic identities.
• Exact perfect-square root → combine nearby squares and unit-digit clues.
• Options available → eliminate impossible unit digits before calculation.
21. Common Exam Traps
Trap 1:
Making every prime exponent larger instead of changing only the odd exponents.
Trap 2:
For least addition, using the previous perfect square instead of the next one.
Trap 3:
For least subtraction, using the next perfect square instead of the previous one.
Trap 4:
Assuming the LCM of several numbers is automatically a perfect square.
Trap 5:
Using the unit digit as complete proof of a square root.
Trap 6:
Appending 25 in the ending-5 shortcut without first multiplying the preceding part by its next integer.
Trap 7:
Confusing the least multiplier with the least number that must be added.
22. Quick Revision
Remember:
• Perfect square → every prime exponent is even.
• Least multiplier → multiply the prime factors having odd exponents.
• Least divisor → divide by the product of factors responsible for odd exponents.
• Least addition → next perfect square minus the number.
• Least subtraction → number minus previous perfect square.
• For several divisibility conditions, find the LCM first and then make it a perfect square.
• Number ending in 5: multiply the preceding part by its next integer and append 25.
• (100±a)2 gives quick squares near 100.
• Next square = current square + next odd number.
• Previous square = current square − previous odd difference.
• Unit digit of a perfect square narrows possible unit digits of its root.
• A perfect square ending in 25 has an integer square root ending in 5.
• Use nearby known squares before doing lengthy calculation.
23. Verified Previous-Year Questions
RRB NTPC PYQ
Least Multiplier
1 April 2021 · CBT-I · Shift 2
Q1. What is the least number by which 588 must be multiplied so that the product becomes a perfect square?
A. 2
B. 3
C. 1
D. 5
Correct Answer: B. 3
588 = 22 × 3 × 72.
Only the exponent of 3 is odd.
Therefore multiply by 3:
588 × 3 = 1764 = 422.
Required number = 3.
RRB ALP PYQ
Least Divisor
30 August 2018 · Shift 2
Q2. By which least number should 1568 be divided so that the quotient becomes a perfect square?
A. 5
B. 6
C. 3
D. 2
Correct Answer: D. 2
1568 = 25 × 72.
Divide by one factor 2:
1568 ÷ 2
= 784
= 282.
Therefore the least divisor is 2.
RRB NTPC PYQ
Least Subtraction
30 December 2020 · CBT-I · Shift 2
Q3. Find the least number that must be subtracted from 60065 to make it a perfect square.
A. 40
B. 30
C. 35
D. 20
Correct Answer: A. 40
2452 = 60025.
Therefore:
60065 − 60025 = 40.
So 40 must be subtracted.
RRB NTPC PYQ
Least Perfect Square Multiple
13 June 2022 · CBT-II Level 2 · Shift 1
Q4. What is the least perfect square that is divisible by each of 27, 54 and 72?
A. 1296
B. 1225
C. 1369
D. 1156
Correct Answer: A. 1296
LCM of 27, 54 and 72 = 216.
216 = 23 × 33.
To make all exponents even, multiply by 2 × 3 = 6.
216 × 6 = 1296 = 362.
Therefore the required number is 1296.
24. Practice MCQs
Practice MCQ
Q1. What is the least number by which 432 must be multiplied to make it a perfect square?
A. 2
B. 3
C. 6
D. 12
Correct Answer: B. 3
432 = 24×33. Multiply by 3 to obtain 24×34 = 1296 = 362.
Practice MCQ
Q2. What is the least number by which 972 must be divided to obtain a perfect square?
A. 2
B. 3
C. 6
D. 9
Correct Answer: B. 3
972 = 22×35. Dividing by 3 gives 324 = 182.
Practice MCQ
Q3. What is the least number to be added to 1450 to make it a perfect square?
A. 6
B. 49
C. 71
D. 81
Correct Answer: C. 71
The next perfect square is 392 = 1521. Therefore 1521−1450 = 71.
Practice MCQ
Q4. What is the least number to be subtracted from 1450 to make it a perfect square?
A. 4
B. 6
C. 10
D. 14
Correct Answer: B. 6
382 = 1444. Therefore 1450−1444 = 6.
Practice MCQ
Q5. What is the least perfect square divisible by 18, 24 and 30?
A. 1800
B. 2400
C. 3600
D. 7200
Correct Answer: C. 3600
LCM = 360 = 23×32×5. Multiply by 10 to obtain 3600 = 602.
Practice MCQ
Q6. Find 852.
A. 7025
B. 7125
C. 7225
D. 7325
Correct Answer: C. 7225
8×9 = 72 and append 25. Therefore 852 = 7225.
Practice MCQ
Q7. Find 982.
A. 9504
B. 9604
C. 9704
D. 9804
Correct Answer: B. 9604
(100−2)2 = 10000−400+4 = 9604.
Practice MCQ
Q8. Find √4489.
A. 63
B. 65
C. 67
D. 69
Correct Answer: C. 67
672 = 4489. Therefore √4489 = 67.
Practice MCQ
Q9. Find √7744.
A. 82
B. 84
C. 86
D. 88
Correct Answer: D. 88
882 = 7744.
Practice MCQ
Q10. If 502 = 2500, find 492 using the consecutive-square shortcut.
A. 2399
B. 2401
C. 2403
D. 2499
Correct Answer: B. 2401
492 = 502−99 = 2500−99 = 2401.
1. Perfect Square निर्माण की मूल अवधारणा
किसी positive integer का prime factorisation करने पर यदि प्रत्येक prime factor की exponent even हो, तो वह number perfect square होता है।
Fundamental Rule:
यदि:
N = paqbrc,
तो N perfect square तभी होगा जब a, b, c, ... सभी even हों।
उदाहरण:
72 = 23 × 32।
2 की exponent odd है, इसलिए 72 perfect square नहीं है।
2. Perfect Square बनाने के लिए Least Multiplication
Method:
1. Number का prime factorisation करें।
2. Odd exponents वाले prime factors identify करें।
3. प्रत्येक odd exponent को even बनाने के लिए minimum required factors से multiply करें।
उदाहरण:
432 को perfect square बनाने के लिए least multiplier ज्ञात करें।
432 = 24 × 33
3 की exponent odd है।
इसलिए 3 से multiply करें:
432 × 3 = 1296 = 362
Required number = 3।
Shortcut:
Odd exponents वाले prime factors का product ही least multiplier होता है।
3. Perfect Square बनाने के लिए Least Division
Method:
Prime factorisation में जिन primes की exponents odd हैं, उनसे आवश्यक factors divide करें ताकि remaining exponents even हो जाएँ।
उदाहरण:
972 = 22 × 35।
3 की exponent odd है।
972 ÷ 3 = 324 = 182।
Least divisor = 3।
Exam Trap:
सभी prime factors से multiply या divide करने की आवश्यकता नहीं होती। केवल odd exponents को correct करना होता है।
4. Perfect Square बनाने के लिए Least Addition
Rule:
यदि:
n2 < N < (n+1)2,
तो least addition होगा:
(n+1)2 − N
उदाहरण:
1450 में least कितना add करें?
382 = 1444
392 = 1521
Required addition:
1521−1450 = 71।
5. Perfect Square बनाने के लिए Least Subtraction
Rule:
यदि:
n2 < N < (n+1)2,
तो least subtraction होगा:
N−n2
उदाहरण:
1450 के लिए previous perfect square:
382 = 1444।
1450−1444 = 6।
Fast Strategy:
Addition के लिए next perfect square पर जाएँ।
Subtraction के लिए previous perfect square पर जाएँ।
6. Addition या Subtraction में कौन छोटा है?
Method:
N और उसके previous perfect square का difference निकालें तथा N और next perfect square का difference निकालें। दोनों compare करें।
उदाहरण:
1450 के लिए:
Previous square difference = 6
Next square difference = 71
इसलिए केवल 6 subtract करना smaller adjustment है।
7. किसी Number से Divisible Least Perfect Square
Method:
1. Number का prime factorisation करें।
2. Odd exponents को even बनाने के लिए minimum factors multiply करें।
उदाहरण:
360 से divisible least perfect square ज्ञात करें।
360 = 23 × 32 × 5
Multiply by 2×5 = 10.
360×10 = 3600 = 602।
Required number = 3600।
8. कई Numbers से Divisible Least Perfect Square
Method:
1. सभी numbers का LCM निकालें।
2. LCM का prime factorisation करें।
3. Odd exponents को even बनाने के लिए minimum factors multiply करें।
उदाहरण:
18, 24 एवं 30 से divisible least perfect square ज्ञात करें।
LCM = 360
= 23 × 32 × 5
Multiply by 2×5 = 10.
Required number = 360×10 = 3600।
Common Mistake:
LCM स्वयं perfect square होना आवश्यक नहीं है। LCM निकालने के बाद भी prime exponents check करें।
9. Prime Exponents से Least Multiplier
Fast Rule:
यदि:
N = 25 × 34 × 53 × 72,
तो odd exponents 2 एवं 5 की हैं।
Least multiplier = 2×5 = 10।
Observation:
Exponent का exact size नहीं, बल्कि उसका even या odd होना महत्वपूर्ण है।
10. Prime Exponents से Least Divisor
Fast Rule:
यदि:
N = 25 × 34 × 53 × 72,
तो 2×5 = 10 से divide करने पर remaining exponents सभी even हो जाएँगी।
11. 5 पर समाप्त Number का Quick Square
Shortcut:
5 पर समाप्त number के लिए:
1. Last digit 5 हटाएँ।
2. Remaining number को उसके next integer से multiply करें।
3. Result के अंत में 25 लगाएँ।
उदाहरण:
852:
8×9 = 72
अंत में 25 लगाएँ:
852 = 7225।
उदाहरण:
1152:
11×12 = 132
Append 25:
1152 = 13225।
12. 100 के निकट Numbers का Square
Identity:
(100±a)2
= 10000±200a+a2
उदाहरण:
982
= (100−2)2
= 10000−400+4
= 9604।
उदाहरण:
1032
= (100+3)2
= 10609।
13. Convenient Base के निकट Number का Square
Identities:
(a+b)2 = a2+2ab+b2
(a−b)2 = a2−2ab+b2
उदाहरण:
522
= (50+2)2
= 2500+200+4
= 2704।
14. Known Square से Next Square
Rule:
(n+1)2 = n2+2n+1
उदाहरण:
402 = 1600 हो, तो:
412
= 1600+81
= 1681।
Shortcut:
Next square प्राप्त करने के लिए next odd number add करें।
15. Known Square से Previous Square
Rule:
(n−1)2 = n2−(2n−1)
उदाहरण:
502 = 2500 हो, तो:
492
= 2500−99
= 2401।
16. Nearby Squares द्वारा Fast Square-Root Identification
उदाहरण:
√4489 ज्ञात करें।
602 = 3600
702 = 4900
672
= (60+7)2
= 3600+840+49
= 4489।
इसलिए:
√4489 = 67।
17. Unit Digit से Square Root की Possibilities
Unit-Digit Pairs:
Square का unit digit 1 → root का unit digit 1 या 9 हो सकता है।
4 → 2 या 8
5 → 5
6 → 4 या 6
9 → 3 या 7
0 → 0
Important:
Unit digit केवल possibilities कम करता है; complete square root हमेशा अकेले इससे नहीं मिलता।
18. Four-Digit Perfect Square का Quick Square Root
Strategy:
1. Number को nearby known squares के बीच locate करें।
2. Root का tens range identify करें।
3. Square के unit digit से possible unit digits निकालें।
4. बची हुई possibilities test करें।
उदाहरण:
√7744 ज्ञात करें।
802 = 6400
902 = 8100
इसलिए root 80 एवं 90 के बीच है।
7744 का unit digit 4 है, इसलिए root 2 या 8 पर समाप्त होगा।
Possible roots: 82 एवं 88।
882 = 7744।
इसलिए √7744 = 88।
19. 25 पर समाप्त Perfect Square का Root
Observation:
यदि perfect square 25 पर समाप्त होता है, तो उसका integer square root 5 पर समाप्त होगा।
उदाहरण:
√5625 ज्ञात करें।
Root 70 एवं 80 के बीच है और 5 पर समाप्त होना चाहिए।
इसलिए possible root = 75।
752 = 5625।
अतः √5625 = 75।
20. Fastest Method कैसे चुनें?
Exam Strategy:
• Prime exponents दिए हों → exponent balancing करें।
• Least addition/subtraction → neighbouring perfect squares देखें।
• कई divisibility conditions हों → पहले LCM निकालें।
• Number 5 पर समाप्त हो → ending-5 shortcut लगाएँ।
• Number 10, 50, 100 आदि के पास हो → algebraic identity use करें।
• Exact square root हो → nearby squares + unit digit use करें।
• Options हों → impossible unit digits पहले eliminate करें।
21. Common Exam Traps
Trap 1:
केवल odd exponents को correct करने के बजाय सभी exponents बदल देना।
Trap 2:
Least addition में previous perfect square use करना।
Trap 3:
Least subtraction में next perfect square use करना।
Trap 4:
LCM को बिना check किए perfect square मान लेना।
Trap 5:
Unit digit को complete proof मान लेना।
Trap 6:
Ending-5 shortcut में preceding part को next integer से multiply किए बिना 25 append करना।
Trap 7:
Least multiplier एवं least addition को एक जैसा समझना।
22. Quick Revision
एक नज़र में:
• Perfect square में सभी prime exponents even होती हैं।
• Least multiplier = odd exponents वाले prime factors का product।
• Least divisor = odd exponents को remove करने वाला minimum product।
• Least addition = next perfect square − given number।
• Least subtraction = given number − previous perfect square।
• Multiple divisibility conditions में पहले LCM निकालें, फिर उसे perfect square बनाएँ।
• 5 पर ending number का square: preceding part × next integer, फिर 25 append करें।
• (100±a)2 near-100 calculations को fast बनाता है।
• Next square = current square + next odd number।
• Previous square = current square − corresponding odd difference।
• Perfect square का unit digit root के possible unit digits बताता है।
• 25 पर ending perfect square का integer root 5 पर समाप्त होता है।
• Lengthy calculation से पहले nearby known squares देखें।
23. Verified Previous-Year Questions
RRB NTPC PYQ
Least Multiplier
1 अप्रैल 2021 · CBT-I · Shift 2
प्रश्न 1. 588 को किस least number से multiply करने पर product perfect square बनेगा?
A. 2
B. 3
C. 1
D. 5
सही उत्तर: B. 3
588 = 22 × 3 × 72।
केवल 3 की exponent odd है।
588 × 3 = 1764 = 422।
Required number = 3।
RRB ALP PYQ
Least Divisor
30 अगस्त 2018 · Shift 2
प्रश्न 2. 1568 को किस least number से divide करने पर quotient perfect square बनेगा?
A. 5
B. 6
C. 3
D. 2
सही उत्तर: D. 2
1568 = 25 × 72।
1568 ÷ 2 = 784 = 282।
Least divisor = 2।
RRB NTPC PYQ
Least Subtraction
30 दिसंबर 2020 · CBT-I · Shift 2
प्रश्न 3. 60065 में से कौन-सा least number subtract करने पर perfect square प्राप्त होगा?
A. 40
B. 30
C. 35
D. 20
सही उत्तर: A. 40
2452 = 60025।
60065−60025 = 40।
इसलिए 40 subtract करना होगा।
RRB NTPC PYQ
Least Perfect Square Multiple
13 जून 2022 · CBT-II Level 2 · Shift 1
प्रश्न 4. 27, 54 एवं 72 में से प्रत्येक से divisible least perfect square कौन-सा है?
A. 1296
B. 1225
C. 1369
D. 1156
सही उत्तर: A. 1296
27, 54 एवं 72 का LCM = 216।
216 = 23 × 33।
Perfect square बनाने के लिए 2×3 = 6 से multiply करें।
216×6 = 1296 = 362।
Required number = 1296।
24. Practice MCQs
Practice MCQ
प्रश्न 1. 432 को किस least number से multiply करने पर perfect square बनेगा?
A. 2
B. 3
C. 6
D. 12
सही उत्तर: B. 3
432 = 24×33। 3 से multiply करने पर 1296 = 362 प्राप्त होता है।
Practice MCQ
प्रश्न 2. 972 को किस least number से divide करने पर perfect square मिलेगा?
A. 2
B. 3
C. 6
D. 9
सही उत्तर: B. 3
972 = 22×35। 972÷3 = 324 = 182।
Practice MCQ
प्रश्न 3. 1450 में least कितना add करने पर perfect square मिलेगा?
A. 6
B. 49
C. 71
D. 81
सही उत्तर: C. 71
Next perfect square 392 = 1521 है। 1521−1450 = 71।
Practice MCQ
प्रश्न 4. 1450 में से least कितना subtract करने पर perfect square मिलेगा?
A. 4
B. 6
C. 10
D. 14
सही उत्तर: B. 6
382 = 1444। इसलिए 1450−1444 = 6।
Practice MCQ
प्रश्न 5. 18, 24 एवं 30 से divisible least perfect square कौन-सा है?
A. 1800
B. 2400
C. 3600
D. 7200
सही उत्तर: C. 3600
LCM = 360। इसे perfect square बनाने के लिए 10 से multiply करें। 3600 = 602।
Practice MCQ
प्रश्न 6. 852 ज्ञात करें।
A. 7025
B. 7125
C. 7225
D. 7325
सही उत्तर: C. 7225
8×9 = 72 और अंत में 25 लगाएँ। इसलिए 852 = 7225।
Practice MCQ
प्रश्न 7. 982 ज्ञात करें।
A. 9504
B. 9604
C. 9704
D. 9804
सही उत्तर: B. 9604
(100−2)2 = 10000−400+4 = 9604।
Practice MCQ
प्रश्न 8. √4489 ज्ञात करें।
A. 63
B. 65
C. 67
D. 69
सही उत्तर: C. 67
672 = 4489। इसलिए √4489 = 67।
Practice MCQ
प्रश्न 9. √7744 ज्ञात करें।
A. 82
B. 84
C. 86
D. 88
सही उत्तर: D. 88
882 = 7744।
Practice MCQ
प्रश्न 10. यदि 502 = 2500 है, तो consecutive-square shortcut से 492 ज्ञात करें।
A. 2399
B. 2401
C. 2403
D. 2499
सही उत्तर: B. 2401
492 = 502−99 = 2500−99 = 2401।