Question

Square root of 196 by repeated subtraction? how to do this?

Answer 1

Step-by-step explanation:

196-1,196-2,196-3,196-4...196-82=14(sqrt of 196)

Answer 2

Square root of 196 = 14

GIVEN:- Perfect square = 196; Method =Repeated Subtraction Method

TO FIND:- Square root of 196

SOLUTION:-

As we know, In the repeated subtraction method, we have to subtract successive odd numbers from the square number until we get zero as the difference.

$196 - 1 = 195$

$195 - 3 = 192$

$192 - 5 = 187$

$187 - 7 = 180$

$180 - 9 = 171$

$171 - 11 = 160$

$160 - 13 = 147$

$147 - 15 = 132$

$132 - 17 = 115$

$115 - 19 = 96$

$96 - 21 = 75$

$75 - 23 = 52$

$52 - 25 = 27$

$27 - 27 = 0$

• Since the last difference is zero, 196 is a perfect square.
• The square root of 196 is 14 as we have performed repeated subtraction 14 times and after the 14th subtraction, the remainder is zero.

Hence, Square root of 196 = 14