# 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) $\sqrt{625}$ = ?

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′.

Questions 2) $\sqrt{784}$ = ?

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.

Questions 3) $\sqrt{576}$ = ?

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

Questions 4) $\sqrt{961}$ = ?

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

## Square Root of 4 Digit Number

Questions 1) $\sqrt{1089}$ = ?

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.

Questions 2) $\sqrt{1681}$ = ?

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.

Questions 3) $\sqrt{3249}$ = ?

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.

Questions 4) $\sqrt{7225}$ = ?

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.

Questions 5) $\sqrt{8464}$ = ?

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.

## Square root of 5 Digit Number

Questions 1) $\sqrt{50176}$ = ?

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.

Questions 2) $\sqrt{105625}$ = ?

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.

Questions 3) $\sqrt{16129}$ = ?

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.

$\sqrt{2}$ = 1.414

$\sqrt{3}$ = 1.732

$\sqrt{5}$ = 2.646

$\sqrt{7}$ = 2.449

Example

$\sqrt{50}$ = ?

Solution:

We can write

$\sqrt{50}=\sqrt{5\times 5\times 2}$

= $(\sqrt{5})^{2}\times \sqrt{2}=5\sqrt{2}=5\times 1.414$ = 7.07

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