Question

A perfect square is the product of any positive whole number used as a factor exactly two times. [Example: 49 is a perfect square because 7 × 7 = 49] The positive whole number N, when multiplied by 150, is a perfect square. What is the least possible positive whole number value for the number N?

5E

Answer 1

N=6

Explanation:

You need to prime factorize 150. 150 = 3*5*2*5.

x*x=perfect square.

What we have done so far is we have split 150 into a few digits

You can add 5 to one box and 5 to the other.

Next if we add 3 to one box and 2 to the other box, then they wont be equal.

Let's try 5*6 and 5.

6 is missing from the second box, so N must be 6 to create a perfect square.

The perfect square is 900 and 30*30 = 900, so it is a perfect square.