#### Question

For the following number, find the smallest whole number by which it should be multiplied so as to get a perfect square number. Also find the square root of the square number so obtained.

180

#### Solution

180 can be factorised as follows.

180 = __2 × 2__ × __3 × 3__ × 5

Here, prime factor 5 does not have its pair. If 5 gets a pair, then the number will become a perfect square. Therefore, 180 has to be multiplied with 5 to obtain a perfect square.

180 × 5 = 900 = __2 × 2__ × __3 × 3__ × __5 × 5__

Therefore, 180 × 5 = 900 is a perfect square.

∴ `sqrt(900)` 2 x 3 x 5 = 30

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Solution For the Following Number, Find the Smallest Whole Number by Which It Should Be Multiplied So as to Get a Perfect Square Number. Also Find the Square Root of the Square Number So Obtained. 180 Concept: Square Roots - Finding Square Root Through Prime Factorisation.