Question

exercises simplify the quotient. 50. \\(\frac{\sqrt{32}}{\sqrt{5}}\\)

Explanation:

Step1: Combine radicals into one

$\frac{\sqrt{32}}{\sqrt{5}} = \sqrt{\frac{32}{5}}$

Step2: Rationalize the denominator

$\sqrt{\frac{32}{5}} = \sqrt{\frac{32 \times 5}{5 \times 5}} = \sqrt{\frac{160}{25}}$

Step3: Simplify the square root

$\sqrt{\frac{160}{25}} = \frac{\sqrt{16 \times 10}}{5} = \frac{4\sqrt{10}}{5}$

Answer:

$\frac{4\sqrt{10}}{5}$