# How do you simplify 8/sqrt(8)?

May 14, 2015

Both the numerator and denominator of a fraction can be multiplied by the same real number (not equal to zero), without changing the value of a fraction.

For instance, $\frac{3}{4} = \frac{3 \cdot 6}{4 \cdot 6} = \frac{3 \cdot 0.123456}{4 \cdot 0.123456}$

Let's use this rule and multiply the numerator and the denominator of our fraction by $\sqrt{8}$:

$\frac{8}{\sqrt{8}} = \frac{8 \cdot \sqrt{8}}{\sqrt{8} \cdot \sqrt{8}} = \frac{8 \cdot \sqrt{8}}{8}$

Additionally, both the numerator and denominator of a fraction can be divided by the same real number (not equal to zero), without changing the value of a fraction.

Let's divide both the numerator and the denominator of our fraction by $8$:

$\frac{8 \cdot \sqrt{8}}{8} = \frac{\sqrt{8}}{1} = \sqrt{8}$

$\therefore , \frac{8}{\sqrt{8}} = \sqrt{8}$

May 14, 2015

$\frac{8}{\sqrt{8}} = {\left(\sqrt{8}\right)}^{2} / \sqrt{8} = \sqrt{8} = \sqrt{4 \cdot 2} = 2 \sqrt{2}$