Question

which sum is irrational?
a ( pi + 18 )
b ( sqrt{25} + 1.75 )
c ( sqrt{4} + 5.5 )
d ( sqrt{36} + sqrt{9} )

Explanation:

Step1: Analyze Option A

$\pi$ is an irrational number, and 18 is a rational number. The sum of an irrational number and a rational number is irrational. So $\pi + 18$ is irrational.

Step2: Analyze Option B

$\sqrt{25}=5$, which is rational, and 1.75 is also rational. The sum of two rational numbers is rational. So $\sqrt{25}+1.75 = 5 + 1.75=6.75$, which is rational.

Step3: Analyze Option C

$\sqrt{4}=2$, which is rational, and 5.5 is rational. The sum of two rational numbers is rational. So $\sqrt{4}+5.5=2 + 5.5 = 7.5$, which is rational.

Step4: Analyze Option D

$\sqrt{36}=6$ and $\sqrt{9}=3$, both are rational. The sum of two rational numbers is rational. So $\sqrt{36}+\sqrt{9}=6 + 3=9$, which is rational.

Answer:

A. $\boldsymbol{\pi + 18}$