Name: Method of Estimating the Square Roots of Numbers
Uploaded: 2019-07-19
Duration: 6 min 15 s
Description: How to figure out the nearest square root of a non-perfect square number or guessing the square root of a perfect square number? Let's learn in this video.

Question

Find the square root of the following, correct to three places of decimal:

4 \frac{2}{3}

Accepted Answer

We have to find out the square root of $4 \frac{2}{3}$ correct to three decimal places.

So, $\sqrt{4 \frac{2}{3}} = \sqrt{\frac{14}{3}}$

First we will add zero to right side of $14$ and $3$ using decimal point after that pair of digits of obtained number from right to left for whole number part and from left to right for decimal part.

So, $14 = 14.000000$

Pairing the digits, we get

$14 = 14.00$ $00$ $00$

Division method:

$\begin{matrix} 3 & . & 7 & 4 & 1 \\ 3 & 1 & 4 & . & 0 & 0 & 0 & 0 & 0 & 0 \\ + 3 & - & 9 \\ 67 & 5 & 0 & 0 \\ + 7 & - & 4 & 6 & 9 \\ 744 & 3 & 1 & 0 & 0 \\ + 4 & 2 & 9 & 7 & 6 \\ 7481 & 1 & 2 & 4 & 0 & 0 \\ + 1 & 7 & 4 & 8 & 1 \\ 4 & 9 & 1 & 9 \end{matrix}$ $\begin{matrix} 1 & . & 7 & 3 & 2 \\ 1 & 3 & . & 0 0 & 0 0 & 0 0 \\ + 1 & - & 1 \\ 27 & 2 & 0 & 0 \\ + 7 & - & 1 & 8 & 9 \\ 343 & 1 & 1 & 0 0 \\ + 3 & - & 1 & 0 & 2 9 \\ 3462 & 7 1 & 0 0 \\ + 2 & 6 9 & 2 4 \\ 3464 & 1 & 7 6 \end{matrix}$

Hence, the square root of $4 \frac{2}{3}$ correct to three place of decimal is $\frac{3.741}{1.732} = 2.160$

Find the square root of the following, correct to three places of decimal: $4 \frac{2}{3}$

Important Questions on Squares and Square Roots

Learn and Prepare for any exam you want !

Find the square root of the following, correct to three places of decimal: 423

Important Questions on Squares and Square Roots

Learn and Prepare for any exam you want !

Find the square root of the following, correct to three places of decimal: $4 \frac{2}{3}$