Question

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 ?

Answer 1

Rational numbers are numbers that can be represented as a fraction of two integers. For  $\sqrt{60 + n}$ and $\sqrt{2n + 28}$ to be rational, the smallest value of n is 4

The correct expressions are:

$\sqrt{60 + n}$ and $\sqrt{2n + 28}$

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 $n =1$

$\sqrt{60 + n} = \sqrt{60 + 1} = \sqrt{61} = 7.810249....$

7.810249... is not rational

When $n=2$

$\sqrt{60 + n} = \sqrt{60 + 2} = \sqrt{62} = 7.87400....$

7.87400... is not rational

When $n=3$

$\sqrt{60 + n} = \sqrt{60 + 3} = \sqrt{63} = 7.93725....$

7.93725... is not rational

When $n=4$

$\sqrt{60 + n} = \sqrt{60 + 4} = \sqrt{64} = 8$

8 is rational

So, we evaluate the second expression for $n=4$

$\sqrt{2n + 28} = \sqrt{2\times4+ 28} = \sqrt{36} = 6$

The above is also rational for $n =4$

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

Read more about rational numbers at:

https://brainly.com/question/13345886