Question

Find the smallest number by which 180 should be

multiply to get a perfect square. Also find the square root of

the number so obtained.​

Answer 1

Answer:

20 .

please thanks my answer a lot of times

Answer 2

Answer:

SOLUTION

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.