Hi Peter,

Let me ask a different question.

Is the square root of 15 × 48 an integer?

You can answer this by looking at the prime factorization of 15 × 48.

15 × 48 = 3 × 5 × 2 × 2 × 2 × 2 × 3 = 2⁴ × 3² × 5¹

The square root of 2⁴ is 2² and the square root of 3² is 3 but the square root of 5¹ is not an integer so the square root of 15 × 48 = 2⁴ × 3² × 5¹ is not an integer.

Now what about this question?

What is the least possible positive integer-value of n such that square root(15 × n × 48) is an integer?

Now I can see how to do this. In the prime factorization of 15 × n × 48 all the primes need to have an even power. 15 × n × 48 = 2⁴ × 3² × 5¹ × n so if n = 5 then 15 × n × 48 = 2⁴ × 3² × 5² and the square root of 15 × n × 48 is an integer.

Penny