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
