Question

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

Answer 1

The correct answer is 5
Explanation:
180 = 2*90 = 2*10*9 =2*2*3*3*5
If we multiply by 5 we would 180*5 = 900 = 30*30
Rule :
Factorise the number and determine what factors occur twice and what factors only occur once.
In our case we see 2 occurs twice and 3 occurs twice and 5 occurs only once.
This means that we already have the square of 2 and the square of 3.
We need to have a square of 5.
Thus we have to multiply the original number by 5 as above

Now the number obtained by multiplying 5 to 180 is 900 whose square root is 30.