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

Find the square root of

144

and

121

by repeated subtraction method.

Accepted Answer

To find the square root of $144$ .

We know that,

The sum of the first $n$ odd natural numbers is $n^{2}$ . So, in this method, we find the square root by repeatedly subtracting successive odd numbers(starting from $1$ ) from the given square number, till we get zero.

$144 - 1 = 143,$

$143 - 3 = 140,$

$140 - 5 = 135,$

$135 - 7 = 128,$

$128 - 9 = 119,$

$119 - 11 = 108,$

$108 - 13 = 95,$

$95 - 15 = 80,$

$80 - 17 = 63,$

$63 - 19 = 44,$

$44 - 21 = 23,$

$23 - 23 = 0$ .

Here, we get $0$ in the twelfth step.

Therefore, the square root of $144$ is $121$ $\Rightarrow \sqrt{144} = 12$ .

To find the square root of $121$ ,

Similarly, by repeatedly subtracting successive odd numbers(starting from $1$ ) from $121$ , till we get zero as follows:

$121 - 1 = 120,$

$120 - 3 = 117,$

$117 - 5 = 112,$

$112 - 7 = 105,$

$105 - 9 = 96,$

$96 - 11 = 85,$

$85 - 13 = 72,$

$72 - 15 = 57,$

$57 - 17 = 40,$

$40 - 19 = 21,$

$21 - 21 = 0$ .

Here, we get $0$ in the eleventh step.

Therefore, the square root of $121$ is $11$ . $\Rightarrow \sqrt{121} = 11$ .

Find the square root of $144$ and $121$ by repeated subtraction method.

Important Questions on Squares and Square Roots

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