which expression is equivalent to $sqrt{6^{2}+3^{2}}$?\na. $3sqrt{2}$\nb. $9sqrt{2}$\nc. $3sqrt{5}$\nd…

Explanation:

Step1: Calculate the values inside the square - root

First, calculate $6^{2}+3^{2}$. According to the exponent rule $a^{2}=a\times a$, we have $6^{2}=6\times6 = 36$ and $3^{2}=3\times3 = 9$. Then $6^{2}+3^{2}=36 + 9=45$.

Step2: Simplify the square - root

We know that $\sqrt{45}=\sqrt{9\times5}$. According to the square - root property $\sqrt{ab}=\sqrt{a}\times\sqrt{b}$ ($a = 9$, $b = 5$ and $a\geq0$, $b\geq0$), so $\sqrt{45}=\sqrt{9}\times\sqrt{5}=3\sqrt{5}$.

Answer:

C. $3\sqrt{5}$