Square Root Shortcut Nonperfect Squares

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, lets say you want to find √26. Guess what, you can find the square root of this nonperfect square in seconds. Here is how you can do it.

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
12=1
22=4
32=9
42=16
52=25
62=36
72=49
82=64
92=81
102=100
112=121
122=144
132=169
142=196
152=225
162=256
172=289
182=324
192=361
202=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

Also see Shortcut to find the square root of any perfect square

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