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 value of $\sqrt{105.0625}$ . Hence, write down the square root of the following.

$10506.25$

Accepted Answer

Given, $\sqrt{105.0625}$ .

Group the integral part and decimal part by placing bars and using long division method, we get,

$\begin{matrix} 10.25 \\ 1 & 1 05.06 25 \\ - 1 \\ 20 & 005 \\ - 0 \\ 202 & 0506 \\ - 404 \\ 2045 & 10225 \\ - 10225 \\ 2050 & 00000 \end{matrix}$

Therefore, $\sqrt{105.0625} = 10.25$

Further, $\sqrt{10506.25} = \sqrt{105.0625 \times 100}$

We have, $\sqrt{a \times b} = \sqrt{a} \times \sqrt{b}$

$\Rightarrow \sqrt{105.0625 \times 100} = \sqrt{105.0625} \times \sqrt{100}$

$∴ \sqrt{10506.25} = \sqrt{105.0625} \times \sqrt{100}$

$= 10.25 \times 10$ $= 102.5$

Hence, $\sqrt{10506.25} = 102.5$

Find the value of $\sqrt{105.0625}$ . Hence, write down the square root of the following.

$10506.25$

Important Questions on Squares and Square Roots

Learn and Prepare for any exam you want !

Find the value of 105.0625. Hence, write down the square root of the following. 10506.25

Important Questions on Squares and Square Roots

Learn and Prepare for any exam you want !

Find the value of $\sqrt{105.0625}$ . Hence, write down the square root of the following.

$10506.25$