Name: Estimation of Square Roots
Uploaded: 2019-07-19
Duration: 6 min 2 s
Description: For not-perfect squares, we can estimate their square root to the closest whole number. Learn how to estimate the square root of non-perfect squares.

Question

Using repeated subtraction method, find the square root of the following number.

$144$

Accepted Answer

Given,

$144$

Recall Property $9$ of a square which states that the square of a number $n$ can be written as the sum of the first $n$ odd numbers.

We will use this property to find the square root of a given perfect square as follows:

From the given number, subtract the odd numbers $1, 3, 5, 7, 9 . . . . . . . .$ one-by-one. If the given number is a perfect square, we will get zero after some subtractions. When we get a zero, we count the number of times the subtraction is done and write it as the square root of the given number.

Thus,

$144 - 1 = 143 143 - 3 = 140 140 - 5 = 135 135 - 7 = 128 128 - 9 = 119 119 - 11 = 108 108 - 13 = 95 95 - 15 = 80 80 - 17 = 63 63 - 19 = 44 44 - 21 = 23 23 - 23 = 0$

Since the last difference is zero, $144$ is a perfect square.

Hence, the square root of $144$ is $12$ as we have performed repeated subtraction $12$ times and after the $12 t h$ subtraction, the remainder is zero.

Using repeated subtraction method, find the square root of the following number.

$144$

Important Questions on Squares and Square Roots

Learn and Prepare for any exam you want !

Using repeated subtraction method, find the square root of the following number. 144

Important Questions on Squares and Square Roots

Learn and Prepare for any exam you want !

Using repeated subtraction method, find the square root of the following number.

$144$