# Square Root Shortcut Nonperfect Squares

In the previous trick, we learned how to find the square root of any number which is a perfect square. Now, using this square root shortcut, you can easily find the square root of a nonperfect square. For instance,

## Square Root Shortcut for Nonperfect squares steps

Step1: Find the nearest square less than or greater than a perfect square and find its square root.

Step 2: Now, find the difference between the nearest square and the given number.

Step 3: Multiply the result obtained in step 1 by 2

Step 4: Divide the result obtained in step 2 by the result obtained in step 3.

Step 5: Combine the results of step 1 and step 4 to arrive at your answer.

Remember the below squares

1^{2}=1

2^{2}=4

3^{2}=9

4^{2}=16

5^{2}=25

6^{2}=36

7^{2}=49

8^{2}=64

9^{2}=81

10^{2}=100

11^{2}=121

12^{2}=144

13^{2}=169

14^{2}=196

15^{2}=225

16^{2}=256

17^{2}=289

18^{2}=324

19^{2}=361

20^{2}=400

Let us now see a few examples to understand better

## Examples

Example 1: Find √26

Step 1: Finding the nearest square to number 26. We find that 25 is the nearest square to 26. √25 =5

Step 2: Finding the difference between the nearest square and the given number. Here, 26-25= 1. Difference= 1

Step 3: Multiplying the result obtained in step 1 by 2.

We get, 5 X 2=10

Step 4: Dividing the result obtained in step 2 by result obtained in step 3.

We get, 1/10=0.10

Step 5: Combining the results of step 1 and step 4.

We get, 5 + 0.10= 5.10

Ans √26 = 5.10

Example 1: Find √38

Step 1: Finding the nearest square to number 38. We find that 36 is the nearest square to 38. √36 =6

Step 2: Finding the difference between the nearest square and the given number. Here, 38-36= 2. Difference= 2

Step 3: Multiplying the result obtained in step 1 by 2.

We get, 6 X 2=12

Step 4: Dividing the result obtained in step 2 by result obtained in step 3.

We get, 2/12=0.16

Step 5: Combining the results of step 1 and step 4.

We get, 6 + 0.16= 6.16

Ans √38 = 6.16

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