Question

write $sqrt{\frac{3}{8}}$ as a radical expression in simplest form. $sqrt{\frac{3}{8}} = \square$

Explanation:

Step1: Rationalize the denominator

Multiply numerator and denominator inside the square root by 2 to make the denominator a perfect square.
$$\sqrt{\frac{3}{8}} = \sqrt{\frac{3 \times 2}{8 \times 2}} = \sqrt{\frac{6}{16}}$$

Step2: Split the square root

Separate the square root of the fraction into the fraction of square roots.
$$\sqrt{\frac{6}{16}} = \frac{\sqrt{6}}{\sqrt{16}}$$

Step3: Simplify the perfect square root

Calculate the square root of 16, which is 4.
$$\frac{\sqrt{6}}{\sqrt{16}} = \frac{\sqrt{6}}{4}$$

Answer:

$\frac{\sqrt{6}}{4}$