consider the statement: \the sum of a rational number and an irrational number is always rational.\ choose…

Explanation:

Step1: Recall rational and irrational numbers

A rational number can be written as a fraction $\frac{a}{b}$ where $a,b\in\mathbb{Z}$ and $b\neq0$. Irrational numbers cannot be written as such. $\sqrt{25}=5$ is rational, $\pi,\sqrt{13},\sqrt{17},\sqrt{18},\sqrt{21}$ are irrational.

Step2: Analyze option A

$\sqrt{25}+\pi = 5+\pi$. Here 5 is rational and $\pi$ is irrational. Their sum is irrational.

Step3: Analyze option B

$0.56+\pi$. Since $0.56=\frac{56}{100}$ is rational and $\pi$ is irrational, their sum is irrational.

Step4: Analyze option C

$\frac{7}{8}+\sqrt{13}$. $\frac{7}{8}$ is rational and $\sqrt{13}$ is irrational, so their sum is irrational.

Step5: Analyze option D

$\pi+\sqrt{17}$ is a sum of two irrational numbers, but we need sum of rational - irrational.

Step6: Analyze option E

$0.45 + 0.96=1.41=\frac{141}{100}$ is a sum of two rational numbers.

Step7: Analyze option F

$\sqrt{18}+\sqrt{21}$ is a sum of two irrational numbers, not a sum of rational - irrational.

Answer:

A. $\sqrt{25}+\pi$, B. $0.56+\pi$, C. $\frac{7}{8}+\sqrt{13}$