Question

By what smallest number must 180 be multiplied so that it become a perfect square ? Also find the square root of the number so obtained.​

Answer 1

$prime \: factors \: of \: 180 = 2 \times 2 \times 3 \times 3 \times 5 *5 so \: smallest \: no \: = 5 \\ \\ so \: obtained \: no = 180 \times 5 = 900 \\ square \: root = 2 \times 3 \times 5 = 30$

Answer 2

Hey dude ✌

First we have to do prime factorisation......

180=2×2×3×3×5

We have to place a bar here

Thus, we require one more five to complete the pairs of the factors. The minimum number by which 180 should be multiplied to make it a perfect square;

180×5=900 is the required perfect square.

.

. .

$\sqrt{900} = \sqrt{2 \times 2 \times 3 \times 3 \times 5 \times 5}$

$= 2 \times 3 \times 5 = 30$

30 is the required answer .

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