Question

lesson = radicals and irrational numbers
question 7 of 13
right angled side lengths of 1 and $\sqrt{6}$ are used to represent which radical value?
select an answer:
$\sqrt{3}$
$\sqrt{11}$
$\sqrt{7}$
$\sqrt{5}$
$\sqrt{2}$

Explanation:

Step1: Apply Pythagorean theorem

In a right - angled triangle, \(a^{2}+b^{2}=c^{2}\). Let \(a = 1\) and \(b=\sqrt{6}\). Then \(c^{2}=1^{2}+(\sqrt{6})^{2}\).

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

\(c^{2}=1 + 6\) (since \(1^{2}=1\) and \((\sqrt{6})^{2}=6\)).

Step3: Find \(c\)

\(c^{2}=7\), so \(c=\sqrt{7}\).

Answer:

\(\sqrt{7}\)