Question

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

Answer 1

Answer:

The prime factorisation of 180:

180 = 2 x 2 x 3 x 3 x 5

Grouping the factors into pairs of equal factors, we get:

180 = (2 x 2) x (3 x 3) x 5

The factor, 5 does not have a pair. Therefore, we must multiply 180 by 5 to make a perfect square. The new number is:

(2 x 2) x (3 x 3) x (5 x 5) = 900

Taking one factor from each pair on the LHS, the square root of the new number is 2 x 3 x 5, which is equal to 30.

Step-by-step explanation:

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