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.

sqrt1

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.

sqrt2

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

sqrt3

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

sqrt5

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

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

sqrt7

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

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

Example: √(33489) = ?

sqrt8

Unit digit will be 3 or 7.

Since, 182 < 334 < 192

So, square root will be 183 or 187.

Now consider 18 and 19.

sqrt9

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

This trick in only helpful for finding out square root of a perfect square.

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