Question

find the smallest number by which 252 must be multiplied to get a perfect square
step by step pls​

Answer 1

Answer:

7

Step-by-step explanation:

Prime factorisation of 252

= 2x2x3x3x7

.: to obtain perfect square multiply 252 by 7

252x7=1764

√1764 = 42

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Answer 2

QUESTION :-

Find the Smallest Whole Number by which 252 must be Multiplied so as to get a Perfect Square. Also, find the Square Root of the Square Number so obtained -

SOLUTION :-

Prime Factorization of 252 = 2 * 2 * 3 * 3 * 7

To find the Number by which 252 must be Multiplied to get a Perfect Square, convert 252 into a Square Root -

So, Therefore, $\sqrt{252} = \sqrt{2 * 2 * 3 * 3 * 7}$

Here, the Prime Factor 7 has no Pair. If 7 gets a Pair, then the given Number becomes a Perfect Square

∴ 252 must be Multiplied by 7 to get a Perfect Square -

252 * 7 = 1, 764

$\sqrt{1764} = \sqrt{2 * 2 * 3 * 3 * 7 * 7} \\\\\sqrt{1764} = \sqrt{2^2} * \sqrt{3^2} * \sqrt{7^2} \\\\\sqrt{1764} = 2 * 3 *7 \\\\\sqrt{1764} = 42$