Question

simplify the square root. assume all variables represent positive numbers. if the square root is already simplified, so state.
\sqrt{45}

select the correct choice below and, if necessary, fill in the answer box to complete your choice.
\bigcirc a. \sqrt{45} = \square (type an exact answer, using radicals as needed.)
\bigcirc b. the expression is already simplified.

Explanation:

Step1: Factor out perfect square

$45 = 9 \times 5$

Step2: Split radical into product

$\sqrt{45} = \sqrt{9 \times 5} = \sqrt{9} \times \sqrt{5}$

Step3: Simplify perfect square root

$\sqrt{9} = 3$, so $\sqrt{45} = 3\sqrt{5}$

Answer:

A. $\sqrt{45} = 3\sqrt{5}$ (Type an exact answer, using radicals as needed.)