Shortcuts Method for Finding Square Root
Read and Learn this table it help you a lot to solve many problems for finding square root and cube root.
Number

Square

Last digit of square

0

0

0

1

1

1

2

4

4

3

9

9

4

16

6

5

25

5

6

36

6

7

49

9

8

64

4

9

81

1

Find the square root of 3 Digit Number
Questions 1) = ?
Solution:
Step 1: First we need to ignore last two digits of 625.i.e 25
Step 2: Now from the above table, find square of a number which is less than and nearest to 6. That number is 2. So left part of answer will be 2.
Step 3: Since last digit of ’625‘ is ‘5‘. From the above table the last digit of 5 comes from the square 5 .Therefore right part (R) of our answer will be ’5′.
Answer = 25
Questions 2) = ?
Solution:
Step 1: Fist we need to ignore last two digit . i .e 84
Step 2: Now from the above table, find square of a number which is less than and nearest to 7.That number is 2 so left part of answer is 2
Step 3: Since the last digit of '784' is 4 .From the above table the last digit of 4 comes from the square of 2 and 8.Now we have to find whether it is 2 or 8For that, multiply left part answer with 1 added in it means multiply 2 with 2 (2+1) = 6 which is less than 7
So that part of answer will be 2 and 8. right part answer will be bigger of 2 or 8 which is 8.
Answer = 28
Questions 3) = ?
Solution:
Step 1: Fist we need to ignore last two digit . i .e 76
Step 2: Now from the above table, find square of a number which is less than and nearest to 5.That number is 2 so left part of answer is 2
Step 3: Since the last digit of '576' is 6 .From the above table the last digit of 6 comes from the square of 4 and 6.Now we have to find whether it is 4 or 6. For that, multiply left part answer with 1 added in it means multiply 2 with 2 (2+1) = 6 which is greater than 5. It means right part answer will be smaller of 4 or 6 which is 4
The answer = 24
Questions 4) = ?
Solution:
Step 1: Fist we need to ignore last two digit . i .e 61
Step 2: Now from the above table, find square of a number which is less than and nearest to 9 .That number is 3 so left part of answer is 3
Step 3: Since the last digit of '961' is 1 .From the above table the last digit of 1 comes from the square of 1 and 9.Now we have to find whether it is 1 or 9. For that, multiply left part answer with 1 added in it means multiply 3 with 3 (3+1) = 12 which is greater than 9. It means right part answer will be smaller of 1 or 9 which is 1
The Answer = 31
Square Root of 4 Digit Number
Questions 1) = ?
Solution:
Step 1: Fist we need to ignore last two digit . i .e 89
Step 2: Now from the above table, find square of a number which is less than and nearest to 10 .That number is 3 so left part of answer is 3
Step 3: Since the last digit of '1089' is 9 .From the above table the last digit of 9 comes from the square of 3 and 7.Now we have to find whether it is 3 or 7. For that, multiply left part answer with 1 added in it means multiply 3 with 3 (3+1) = 12 which is greater than 10. It means right part answer will be smaller of 3 or 7 which is 3.
Answer = 33
Questions 2) = ?
Solution:
Step 1: Fist we need to ignore last two digit . i .e 81
Step 2: Now from the above table, find square of a number which is less than and nearest to 16 .That number is 4 so left part of answer is 4
Step 3: Since the last digit of '1681' is 1 .From the above table the last digit of 1 comes from the square of 1 and 9.Now we have to find whether it is 1 or 9. For that, multiply left part answer with 1 added in it means multiply 4 with 4 (4+1) = 20 which is greater than 16. It means right part answer will be smaller of 1 or 9 which is 1.
Answer = 41
Questions 3) = ?
Solution:
Step 1: Fist we need to ignore last two digit . i .e 49
Step 2: Now from the above table, find square of a number which is less than and nearest to 32 .That number is 5 so left part of answer is 5
Step 3: Since the last digit of '3249' is 9 .From the above table the last digit of 9 comes from the square of 3 and 7.Now we have to find whether it is 3 or 7. For that, multiply left part answer with 1 added in it means multiply 5 with 5 (5+1) = 50 which is less than 32. It means right part answer will be bigger of 3 or 7 which is 7.
Answer = 57
Questions 4) = ?
Step 1: Fist we need to ignore last two digit . i .e 25
Step 2: Now from the above table, find square of a number which is less than and nearest to 72 .That number is 8 so left part of answer is 8
Step 3: Since the last digit of '7225' is 5 .From the above table the last digit of 5 comes from the square of 5 It means right part answer will be bigger of 3 or 7 which is 5.
Answer = 85
Questions 5) = ?
Step 1 :Fist we need to ignore last two digit . i .e 64
Step 2: Now from the above table, find square of a number which is less than and nearest to 84 .That number is 9 so left part of answer is 9
Step 3: Since the last digit of '8464' is 4 .From the above table the last digit of 5 comes from the square of 2 and 8 Now we have to find whether it is 2 or 8. For that, multiply left part answer with 1 added in it means multiply 9 with 9 (9+1) = 90 which is greater than 84. It means right part answer will be less of 2 or 8 which is 2.
The Answer = 92
Square root of 5 Digit Number
Questions 1) = ?
Step 1: Fist we need to ignore last two digit . i .e 76
Step 2: Now from the above table, find square of a number which is less than and nearest to 501 .That number is 22 so left part of answer is 22
Step 3: Since the last digit of '50176' is 6 .From the above table the last digit of 6 comes from the square of 4 and 6 .Now we have to find whether it is 4 or 6. For that, multiply left part answer with 1 added in it means multiply 22 with 22 (22+1) = 506 which is greater than 501. It means right part answer will be less of 4 or 6 which is 4.
Answer = 224
Questions 2) = ?
Step 1: Fist we need to ignore last two digit . i .e 25
Step 2: Now from the above table, find square of a number which is less than and nearest to 1056 .That number is 32 so left part of answer is 32
Step 3: Since the last digit of '105625' is 5 .From the above table the last digit of 5 comes from the square of 5 .It means right side of answer will be 5.
Answer = 325
Questions 3) = ?
Step 1: Fist we need to ignore last two digit . i .e 29
Step 2: Now from the above table, find square of a number which is less than and nearest to 161 .That number is 12 so left part of answer is 12
Step 3: Since the last digit of '16129' is 9 .From the above table the last digit of 9 comes from the square of 3 and 7 .Now we have to find whether it is 3 or 9. For that, multiply left part answer with 12 added in it means multiply 12 with 12 (12+1) = 156 which is less than 161. It means right part answer will be greater of 3 or 7 which is 7.
Answer = 127
Read and Learn the following term it will help you to solve many problems:
= 1.414
= 1.732
= 2.646
= 2.449
Example
= ?
Solution:
We can write
= = 7.07