Shortcut to Find Square Root of a Number by Top Competitive Institute for Banking, SSC, Railway

Unit Digits of Squares

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

Now from the picture we can say 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.

How to Find Square Root of a Four Digit Number

Let’s learn how to find square root 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?

sqrt4

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!

How to Find Square Root of a Five Digit Number

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) = ?

sqrt6