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 smallest number by which

9408

must be divided to get a perfect square number. Also, find the square root of the number so obtained.

Accepted Answer

Given number is $9408$ . Resolve $9408$ into prime factors.

$\begin{matrix} 2 & 9 & 4 & 0 & 8 \\ 2 & 4 & 7 & 0 & 4 \\ 2 & 2 & 3 & 5 & 2 \\ 2 & 1 & 1 & 7 & 6 \\ 2 & 5 & 8 & 8 \\ 2 & 2 & 9 & 4 \\ 3 & 1 & 4 & 7 \\ 7 & 4 & 9 \\ 7 & 7 \\ 1 \end{matrix}$

So, $9408 = 2 \times 2 \times 2 \times 2 \times 2 \times 2 \times 3 \times 7 \times 7$

If $9408$ is a perfect square, all the prime factors should be paired.

Here, $3$ is unpaired. So $9408$ is not a perfect square.

If $9408$ is divided by $3$ . The number obtained will be a perfect square.

So, $\frac{9408}{3} = 3136$

Hence, $3$ is the smallest number by which $9408$ must be divided, so that the quotient is a perfect square.

Prime factorisation of $3136$ is obtained by removing $3$ from the prime factorisation of $9408$ .

To find the square root of a number, we need to make pairs of similar factors and take the product of prime factors, choosing one factor out of every pair.

$3136 = 2 \times 2 \times 2 \times 2 \times 2 \times 2 \times 7 \times 7$

$\sqrt{3136} =$ $2 \times 2 \times 2 \times 7$ $= 56$

Hence, the square root of quotient $3136$ is $56$ .

Find the smallest number by which $9408$ must be divided to get a perfect square number. Also, find the square root of the number so obtained.

Important Questions on Squares and Square Roots

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