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′.

Answer = 25


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.

Answer = 28


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

The answer = 24


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

The Answer = 31

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.

Answer = 33


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.

Answer = 41


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.

Answer = 57


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.

Answer = 85


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.

The Answer = 92

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.

Answer = 224


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.

Answer = 325


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.

Answer = 127

Read and Learn the following term it will help you to solve many problems:

\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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