Question

Find the smallest number by which

10368

must be divided so that the result is a perfect square. Also, find the square root of the resulting number.

Accepted Answer

Given number is $10368$

First find the prime factors for $10368$

$\begin{matrix} 2 & 10368 \\ 2 & 5184 \\ 2 & 2592 \\ 2 & 1296 \\ 2 & 648 \\ 2 & 324 \\ 2 & 162 \\ 3 & 81 \\ 3 & 27 \\ 3 & 9 \\ 3 \end{matrix}$

$10368 = 2 \times 2 \times 2 \times 2 \times 2 \times 2 \times 2 \times 3 \times 3 \times 3 \times 3$

By grouping the prime factors in equal pairs we get,

$= (2 \times 2) \times (2 \times 2) \times (2 \times 2) \times (3 \times 3) \times (3 \times 3) \times 2$

The smallest number by which $10368$ must be divided so that the quotient becomes a perfect square is $2$ .

The number after division, $\frac{10368}{2} = 5184$

Prime factors for $5184 = 2 \times 2 \times 2 \times 2 \times 2 \times 2 \times 3 \times 3 \times 3 \times 3$

By grouping the prime factors in equal pairs we get,

$= (2 \times 2) \times (2 \times 2) \times (2 \times 2) \times (3 \times 3) \times (3 \times 3)$

$= (72)^{2}$

Hence, the square root of the resulting number is $72$ .

R K Bansal Solutions for Chapter: Squares and Square Roots, Exercise 1: EXERCISE 3(A)

R K Bansal Mathematics Solutions for Exercise - R K Bansal Solutions for Chapter: Squares and Square Roots, Exercise 1: EXERCISE 3(A)

Questions from R K Bansal Solutions for Chapter: Squares and Square Roots, Exercise 1: EXERCISE 3(A) with Hints & Solutions

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