Question

find the smallest number by which 180 must be multiplied so that it becomes a perfect square. also ,find the square root of the perfect square so obtaineds.

Answer 1

Prime factorisation of
180=2×2×3×3×5
if we multiply 180 by5 we will get a perfect square
so the smallest number by which 180 should be multiplied is 5
the number will be 900
so √900= 30

Hope this helps
please mark as brainliest

Answer 2

Given: A number- 180

To find:  (i) The smallest number by which 180 must be multiplied so that it becomes a perfect square

(ii) Square root of the perfect square so obtained

Solution:

(i) Using Prime factorization, 180 can be expressed as:

180 = 2 × 2 × 3 × 3 × 5

We can observe that 5 couldn't be paired in the prime factorization of 180. So, we need to multiply 180 by 5 so that it becomes a perfect square.

(ii) On multiplying 180 by 5, we get

180 × 5 = 900

Using prime factorization, 900 can be expressed as:

900 = 2 × 2 × 3 × 3 × 5 × 5

Square root of 900 = 2 × 3 × 5 = 30 (Product of numbers taken from each pair of identical numbers)

Hence, 5 is the smallest number by which 180 must be multiplied to make it a perfect square and the square root of the number so obtained is 30.