Question

lesson = radicals and irrational numbers question 11 of 13 right angled side lengths of 1 and sqrt{13} are used to represent which radical value? select an answer: sqrt{7} sqrt{13} sqrt{10} sqrt{14} sqrt{6}

Explanation:

Step1: Apply Pythagorean theorem

For a right - angled triangle, \(a^{2}+b^{2}=c^{2}\). Let \(a = 1\) and \(b=\sqrt{13}\). Then \(c^{2}=1^{2}+(\sqrt{13})^{2}\).

Step2: Calculate \(c^{2}\)

\(c^{2}=1 + 13\).

Step3: Find \(c\)

\(c^{2}=14\), so \(c=\sqrt{14}\).

Answer:

\(\sqrt{14}\)