Question

you are given the expressions 76+n and 2n + 26. What is the smallest value of n that will make each number rational?

Answer 1

The smallest value of n is 5.

Explanation:

The expressions provided are:

`1. √(76+n)\\\\2. √(2n+26)`

Rational numbers are those numbers that can be expressed in ratio or fractional form, i.e. in the form of
`(p)/(q)`.

The provided numbers have denominators as 1.

We need to find the minimum value of n to make both the numbers a perfect square.

Consider the first number,

`√(76+n)=√(76+5)=√(81)=9`

The number
`(9)/(1)` is a rational number.

Consider the second number,

`√(2n+26)=√((2*5)+26)=√(36)=6`

The number
`(6)/(1)` is a rational number.

Thus, the smallest value of n is 5.