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By what smallest number should 216 be divided so that the quotient is a perfect square. Also find the square root of the quotient. - Mathematics

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Sum

By what smallest number should 216 be divided so that the quotient is a perfect square. Also find the square root of the quotient.

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Solution

Prime factors of 216 = 2 × 2 × 2 × 3 × 3 × 3

Grouping the factors into pairs of equal factors, we get

216 = 2 × 2 × 2 × 3 × 3 × 3

We find that there is no prime factor to form a pair with 2 and 3.

Therefore, we must divide the number by 6, so that the quotient becomes a perfect square.

If we divide the given number by 2 × 3 i.e. 6, then

New number = `216/6` = 36

Taking one factor from each, we get square root of new number (quotient) = 2 × 3 = 6

Concept: Finding Square Root Through Prime Factorisation
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APPEARS IN

NCERT Mathematics Exemplar Class 8
Chapter 3 Square-Square Root and Cube-Cube Root
Exercise | Q 101 | Page 94

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