Answer:
The smallest value of n is 5.
Step-by-step explanation:
The expressions provided are:
[tex]1. \sqrt{76+n}\\\\2. \sqrt{2n+26}[/tex]
Rational numbers are those numbers that can be expressed in ratio or fractional form, i.e. in the form of [tex]\frac{p}{q}[/tex].
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,
[tex]\sqrt{76+n}=\sqrt{76+5}=\sqrt{81}=9[/tex]
The number [tex]\frac{9}{1}[/tex] is a rational number.
Consider the second number,
[tex]\sqrt{2n+26}=\sqrt{(2\times5)+26}=\sqrt{36}=6[/tex]
The number [tex]\frac{6}{1}[/tex] is a rational number.
Thus, the smallest value of n is 5.
