Question

pythagorean theorem and simplifying radicals practice
11 of 32
simplify.

1. \\(\frac{\sqrt{8}}{\sqrt{3}}\\)

Explanation:

Step1: Rationalize the denominator

Multiply numerator and denominator by $\sqrt{3}$:
$\frac{\sqrt{8}}{\sqrt{3}} \times \frac{\sqrt{3}}{\sqrt{3}} = \frac{\sqrt{8 \times 3}}{\sqrt{3 \times 3}}$

Step2: Simplify the radicals

Simplify the product inside the square roots:
$\frac{\sqrt{24}}{\sqrt{9}} = \frac{\sqrt{4 \times 6}}{3}$

Step3: Simplify $\sqrt{4 \times 6}$

Extract the perfect square factor:
$\frac{2\sqrt{6}}{3}$

Answer:

$\frac{2\sqrt{6}}{3}$