Question

Find the smallest square no. by which 5392 must be divided so that the quotient is a perfect square.
Answer is 337. so do not spam
and explain step by step​

Answer 1

Step-by-step explanation:

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Answer 2

337 is the smallest square no. by which 5392 must be divided so that the quotient is a perfect square

Given :

The number 5392

To find :

The smallest square no. by which 5392 must be divided so that the quotient is a perfect square

Concept :

Step : I - Firstly express the given number as a product of prime factor by using prime

factorisation

Step : II - Make the pair of similar factors such that the both factors in each pair are equal.

Step : III - Take one factor from each pair.

Step : IV - If no factor is left over in grouping (pairs) then the number is perfect square otherwise not

Solution :

Step 1 of 2 :

Prime factorise the given number

Here the given number is 5392

$\begin{gathered}\begin{gathered}\begin{gathered} \:\: \begin{array}{c|c} {\underline{\sf{2}}}&{\underline{\sf{\:\:5392 \:\:}}}\\ {\underline{\sf{2}}}&\underline{\sf{\:\:2696 \:\:}} \\ {\underline{\sf{2}}}&\underline{\sf{\:\:1348 \:\:}} \\\underline{\sf{2}}&\underline{\sf{\:\:674\:\:}}\\\underline{\sf{337}}&\underline{\sf{\:\:337\:\:}} \\ {\underline{\sf{}}}&\underline{\sf{\:\:1\:\:}} \end{array}\end{gathered}\end{gathered}\end{gathered}$

5392 = 2 × 2 × 2 × 2 × 337

∴ 5392 = 2² × 2² × 337

Step 2 of 2 :

Find the smallest square no. by which 5392 must be divided so that the quotient is a perfect square

Since the factor 337 does not have pair

So we need to divide the number 5392 by 337 to make a perfect square

Hence 337 is the smallest square no. by which 5392 must be divided so that the quotient is a perfect square

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