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

1218816

using long division method.

Accepted Answer

We need to find the square root of a number $1218816$ using long division method:

Step 1: Find the largest number whose square is either equal to or just less than $1$ . The number obtained will be the divisor as well as the quotient

$\begin{matrix} 1 \\ 1 & \bar{01} & \bar{21} & \bar{88} & \bar{16} \\ - & 1 \\ 0 & 21 \end{matrix}$

Step 2: Bring down the number under the next bar to the right of the remainder. So, new dividend is $21$

Double the quotient and put it as the new divisor.

$\begin{matrix} 1 \\ 1 & \bar{01} & \bar{21} & \bar{88} & \bar{16} \\ - & 1 \\ 2_ & 0 & 21 \\ - \end{matrix}$

Find the largest possible digit which becomes the new digit in the quotient such that the new divisor is multiplied to new digit in the quotient, the product is less or equal to dividend.

$\begin{matrix} 1 & 1 \\ 1 & \bar{01} & \bar{21} & \bar{88} & \bar{16} \\ - & 1 \\ 21 & 0 & 21 \\ - & 0 & 21 \\ 0 & 88 \end{matrix}$

Continue the process till we get the remainder as $0$ .

$\begin{matrix} 1 & 1 & 0 & 4 \\ 1 & \bar{01} & \bar{21} & \bar{88} & \bar{16} \\ - & 01 \\ 21 & 0 & 21 \\ - & 21 \\ 0 & 88 \\ 0 \\ 2204 & 88 & 16 \\ - & 88 & 16 \\ 0 \end{matrix}$

Hence, $\sqrt{1218816} = 1104$

Find the square root of $1218816$ using long division method.

Important Questions on Squares and Square Roots

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