You are given the expressions square root of 60 n and the square root of 2n 28 what is the smallest value of the n that will make each number rational ?

Rational numbers are numbers that can be represented as a fraction of two integers. For   and to be rational, the smallest value of n is 4

The correct expressions are:

and

For both numbers to be rational, we should be able to represent the numbers as a fraction of two integers.

There are no direct method to solve this, except trial by error.

When

7.810249... is not rational

When

7.87400... is not rational

When

7.93725... is not rational

When

8 is rational

So, we evaluate the second expression for

The above is also rational for

Hence, the smallest value of n that makes each expression rational is  4

Read more about rational numbers at:

link

72 is the answer to this problem