Question

Find the square root of $6084$ by division method.

Accepted Answer

Given number is $6084$ .

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

$60 84$

Step $2$ : Find the largest number whose square is less than or equal to $60$ such that $7^{2} < 60$ .

Step $3$ : Consider $7$ as the divisor and the quotient. Perform division and the remainder obtained is $11$

$\begin{matrix} 7 \\ 7 & 6 & 0 & 8 & 4 \\ - & 4 & 9 \\ 1 & 1 \end{matrix}$

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

Now, $1184$ is the dividend.

$\begin{matrix} 7 \\ 7 & 6 & 0 & 8 & 4 \\ - & 4 & 9 \\ 1 & 1 & 8 & 4 \end{matrix}$

Step $5$ : Double the quotient i.e. $(7 \times 2 = 14)$ and write to the left of $1184$ .

$\begin{matrix} 7 \\ 7 & 6 & 0 & 8 & 4 \\ - & 4 & 9 \\ 14 & 1 & 1 & 8 & 4 \end{matrix}$

Step $6$ : Guess the largest possible digit in the One's place as $b$ such that $14 b \times b$ is equal to the new dividend $1184$ . So, we have $b = 8$ . Perform division in which $1184$ is the dividend, $148$ is the divisor and $8$ is the quotient.

$\begin{matrix} 7 & 8 \\ 7 & 6 & 0 & 8 & 4 \\ - & 4 & 9 \\ 148 & 1 & 1 & 8 & 4 \\ - & 1 & 1 & 8 & 4 \\ 0 \end{matrix}$

$\Rightarrow \sqrt{6084} = 78$

$∴$ The square root of $6084 = 78$

Telangana Board Solutions for Chapter: Square Roots and Cube Roots, Exercise 9: Exercise 9

Telangana Board Mathematics Solutions for Exercise - Telangana Board Solutions for Chapter: Square Roots and Cube Roots, Exercise 9: Exercise 9

Questions from Telangana Board Solutions for Chapter: Square Roots and Cube Roots, Exercise 9: Exercise 9 with Hints & Solutions

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