Question

which of the following is a rational number? a $sqrt{169}$ b $sqrt{17}$ c $sqrt{3}$ d $sqrt{40}$

Explanation:

Step1: Evaluate Option A

$\sqrt{169} = 13$, since $13^2 = 169$

Step2: Evaluate Option B

$\sqrt{17} \approx 4.123$, which is non-terminating, non-repeating

Step3: Evaluate Option C

$\sqrt{3} \approx 1.732$, which is non-terminating, non-repeating

Step4: Evaluate Option D

$\sqrt{40} = 2\sqrt{10} \approx 6.324$, which is non-terminating, non-repeating

Step5: Identify rational number

A rational number can be written as $\frac{p}{q}$ where $p,q$ are integers, $q
eq0$. 13 is $\frac{13}{1}$, so it is rational.

Answer:

A. $\sqrt{169}$