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

We know  :  12 = 1

22 = 4

32 = 9

42 = 16

52 = 25

62 = 36

72 = 49

82 = 64

92 = 81

102 = 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,

32 = 9  which is smaller than 15

And

42 = 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 12 = 1 or  92 = 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  .

• 16
a) 39
b) 42
• 1
thx
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