Question

right angled side lengths of 1 and (sqrt{17}) are used to represent which radical value?

Explanation:

Step1: Apply Pythagorean theorem

If \(1\) and \(\sqrt{17}\) are the legs of a right - triangle, then the hypotenuse \(c=\sqrt{1^{2}+(\sqrt{17})^{2}}=\sqrt{1 + 17}=\sqrt{18}\).
If \(1\) is a leg and \(\sqrt{17}\) is the hypotenuse, then the other leg \(b=\sqrt{(\sqrt{17})^{2}-1^{2}}=\sqrt{17 - 1}=\sqrt{16}=4\) (not in the options).

Answer:

\(\sqrt{18}\)