Question

combine these radicals.
$8\sqrt{5} + 2\sqrt{45}$
options: $14\sqrt{5}$, $10\sqrt{5}$, $74\sqrt{45}$, $4\sqrt{5}$

Explanation:

Step1: Simplify $\sqrt{45}$

$\sqrt{45} = \sqrt{9 \times 5} = \sqrt{9} \times \sqrt{5} = 3\sqrt{5}$

Step2: Substitute back into expression

$8\sqrt{5} + 2 \times 3\sqrt{5} = 8\sqrt{5} + 6\sqrt{5}$

Step3: Combine like radicals

$8\sqrt{5} + 6\sqrt{5} = (8+6)\sqrt{5} = 14\sqrt{5}$

Answer:

$14\sqrt{5}$