Question

for each of the following number find the smallest whole number by which if we should multiply shows as to get a perfect square number also find the square root of the square number so obtained 180​

Answer 1

Answer:

Step-by-step explanation:

By prime factorization, we get, 180 = (3 x 3) x (2 x 2) x 5

Here, 3 and 2 are in pair but 5 needs a pair to make 180 a perfect square.

So, 180 needs to be multiplied by 5 to become a perfect square.

180×5 =(3 x 3) x (2 x 2) x (5×5)

Therefore, the number 180 has 3 pairs of equal prime factors .

Hence, 900 is a perfect square & √ 900= 3×2×5=30

Hence, the smallest number by which 180 must be multiplied so that the product is a perfect square is 5.

And the square root of the new number is √900=30