First we need to remember unit digits of all squares from 1 to 10. The figure below shows the unit digits of the squares.

As it is clear from the above image that whenever the unit digit of a number is 9, unit digit of the square root of that number will be definitely 3 or 7. Similarly, this can be applied to other numbers with different unit digits.

Let’s learn square root shortcuts by taking different examples.

Example: Find the square root of 4489.

We group the last pair of digits, and the rest of the digits together.

Now, since the unit digit of 4489 is 9. So we can say that unit digit of its square root will be either 3 or 7.

Now consider first two digits i.e. 44. Since 44 comes in between the squares of 6 and 7 (i.e. 6² < 44 < 7²), so we can definitely say that the ten’s digit of the square root of 4489 will be 6.  So far, we can say that the square root will be either 63 or 67.

Now we will find the exact unit digit.

To find the exact unit digit, we consider the ten’s digit i.e. 6 and the next term i.e. 7.

Multiply these two terms

Since, 44 is greater than 42. So square root of 4489 will be the bigger of the two options i.e. 67.
Let us take another example.

Example: What is the square root of 7056?

Unit digit will be 4 or 6.

Since, 8² < 70 < 9²

So the square root will be either 84 or 86.

Now consider 8 and 9

Since, 70 is less than 72. So square root will be the lesser of the two values i.e. 84.

Let’s try it out with five digit numbers now!

We pair the digits up starting from the right side. Since there is one extra left over after two pairs are formed, we club it with the pair closest to it.

Example: √(16641) = ?

Unit digit will be 1 or 9.

Since, 12² < 166 < 13²

So, the square root will definitely be 121 or 129.

Now, consider 12 and 13

Since, 166 is greater the 156, we pick the larger of the options i.e. 129.

Let’s take another example, so that this square root trick will be clear to you.

Example: √(33489) = ?

Unit digit will be 3 or 7.

Since, 18² < 334 < 19²

So, square root will be 183 or 187.

Now consider 18 and 19.

Now, 334 is less than 342. So, the square root will be lesser of the two numbers i.e. 183.

These square root shortcuts to find square root of a number will surely help you in your exams. Now that you have learnt the basics, take different examples and practice some more.