# Find the square root of the following by ones and tens method (a)1521 (b)1764

We know : 1

^{2}= 1

2

^{2}= 4

3

^{2}= 9

4

^{2}= 16

5

^{2}= 25

6

^{2 }= 36

7

^{2}= 49

8

^{2}= 64

9

^{2}= 81

10

^{2}= 100

Step 1: First of all group the number in pairs of 2 starting from the right.

So,

1521 = 15 | 21

Step 2: To get the ten’s place digit , Find the nearest square (equivalent or less than) to the first grouped pair from left and putthe square root of the square.

So,

3

^{2}= 9 which is smaller than 15

And

4

^{2}= 16 which is greater than 15 , So

Tens digit of our solution = " 3 "

Step 3: To get the unit’s place digit of the square root , we look into square number table If number ends in Unit’s place digit of the square root

Here unit digit number = 1 Which is comes when 1

^{2}= 1 or 9

^{2}= 81

Step 4: Multiply the ten’s place digit ( found in step 1 = 3 ) with its consecutive number and compare the result obtained with the first pair of the original number from left.

We get two cases :

Case I : If first pair of the original number > Result obtained on multiplication

Then select the greater number out of the two numbers as the unit’s place digit of the square root.

Case II : If first pair of the original number < the result obtained on multiplication,

Then select the lesser number out of the two numbers as the unit’s place digit of the square root.

Here 3 ( 4 ) = 12

And we know

21 > 12

So, we select greater number in between ( 1 and 9 ) .

Therefore tens digit = 9

And

**$\sqrt{1521}$ = 39 ( Ans )**

Try to find value of $\sqrt{1764}$ similarly and if still have any doubt kindly get back to us , So we can help you precisely .

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