Question

What is the least possible positive integer-value of n such that sqrt{18\cdot n \cdot 34}$ is an integer?

Answer 1

Answer:

n = 17. This means, √(18 x 17 x 34) = √(10404) = 102.

Step-by-step explanation:

An integer is a number that is not a fraction.

Given √(18 x n x 34), for the expression to be an integer, the product must be a perfect square. We are looking for n, the smallest number to multiply 18 x 34 to make it a perfect square. We have:

18 x 34 = 2 x 9 x 2 x 17 = 2 x 3 x 3 x 2 x 17 = 2² x 3² x 17.

From here, we see that we need to multiply an extra 17 to make it a perfect square, therefore n = 17. So we have:

√(18 x 17 x 34) = √(10404) = 102