Question

write the following quotient in simplest form.
\frac{\sqrt{640}}{\sqrt{5}}
\frac{\sqrt{640}}{\sqrt{5}} = \square
(simplify your answer. type an exact answer, using radicals as needed.)

Explanation:

Step1: Combine radicals into one

$\frac{\sqrt{640}}{\sqrt{5}} = \sqrt{\frac{640}{5}}$

Step2: Simplify the fraction inside

$\sqrt{\frac{640}{5}} = \sqrt{128}$

Step3: Factor 128 into perfect square

$\sqrt{128} = \sqrt{64 \times 2}$

Step4: Separate the perfect square

$\sqrt{64 \times 2} = \sqrt{64} \times \sqrt{2} = 8\sqrt{2}$

Answer:

$8\sqrt{2}$