Question

Find the square root of $108241$ by long division method.

Accepted Answer

Given number is $108241$ . To find $\sqrt{108241}$ using long division method, we need to follow the given steps.

Step $1$ : Pair the digits of the given number, starting from units place to the left. Place a bar on each pair of digits.

$10 82 41$

Step $2$ : Find the largest number whose square is less than or equal to $10$ such that $3^{2} < 10$ .

Step $3$ : Consider $3$ as the divisor and the quotient. Perform division and the remainder obtained is $1$ .

$\begin{matrix} 3 \\ 3 & 1 & 0 & 8 & 2 & 4 & 1 \\ - & 9 \\ 1 \end{matrix}$

Step $4$ : Bring down the next pair to the right of the Remainder.

Now, $182$ is the dividend.

$\begin{matrix} 3 \\ 3 & 1 & 0 & 8 & 2 & 4 & 1 \\ - & 9 \\ 1 & 8 & 2 \end{matrix}$

Step $5$ : Double the quotient i.e. $(3 \times 2 = 6)$ and write to the left of $182$ .

$\begin{matrix} 3 \\ 3 & 1 & 0 & 8 & 2 & 4 & 1 \\ - & 9 \\ 6 & 1 & 8 & 2 \end{matrix}$

Step $6$ : Guess the largest possible digit in the Ones place as $b$ such that $6 b \times b$ is less than or equal to the new dividend $182$ . So, we have $b = 2$ . Perform division in which $182$ is the dividend, $62$ is the divisor and $2$ is the quotient.

$\begin{matrix} 3 & 2 \\ 3 & 1 & 0 & 8 & 2 & 4 & 1 \\ - & 9 \\ 62 & 1 & 8 & 2 \\ - & 1 & 2 & 4 \\ 5 & 8 \end{matrix}$

Repeat the process in step $4$ , step $5$ and step $6$ , we will obtain zero as remainder as follows:

$\begin{matrix} 3 & 2 & 9 \\ 3 & 1 & 0 & 8 & 2 & 4 & 1 \\ - & 9 \\ 62 & 1 & 8 & 2 \\ - & 1 & 2 & 4 \\ 649 & 5 & 8 & 4 & 1 \\ - & 5 & 8 & 4 & 1 \\ 0 \end{matrix}$

$\Rightarrow \sqrt{108241} = 329$

$∴$ The square root of $108241 = 329$

M L Aggarwal Solutions for Chapter: Squares and Square Roots, Exercise 5: Check Your Progress

M L Aggarwal Mathematics Solutions for Exercise - M L Aggarwal Solutions for Chapter: Squares and Square Roots, Exercise 5: Check Your Progress

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