Let’s do this by example

###
**
Square root of 17.64 by long division
**

**
**

Therefore,

Square root of 17.64 =
**
4.2
**

###
**
Individual Steps are explained
**

**
Step
**
**
1:
**

- Write the number
- We make pairs from right.

**
For numbers before decimal point,
**

we start from right and make pairs

So, 17 is a pair

**
For numbers
**
**
after
**
**
decimal point,
**

we start from the right of decimal point and make pairs

So, 64 is a pair

**
Step 2:
**

Now we find that number whose

square is less than or equal to 16.

3 × 3 = 9

4 × 4 = 16

5 × 5 = 25

Since 25 > 17, we use 4 × 4.

So writing 4 on left side & top.

& 16 below 17

Now we find remainder,

17 − 16 = 1

**
Step 3:
**

Since next is decimal point

We put a decimal point on top

**
Step
**
**
4
**

Pair 64 comes down

So, our number is now 164

**
Step
**
**
5
**

We multiply the number above by 2

& add a blank after it

So, we write 4 × 2 = 8

8 _

**
Step
**
**
6
**

Find a number which is less than

Or equal to 164

81 × 1 = 81

82 × 2 = 164

Since 82 × 2 = 164. We use that

Thus,

Square root of 17.64 = 4.2

###
**
Square root of 1.125 by long division
**

**
**

Therefore,

Square root of 1.125 =
**
1.060…
**

*
Here, we can find square root
*
*
upto
*
*
more decimal digits.
*

*
But, we stop at 3 digits after decimal point
*