How do you simplify sqrt14-sqrt2/7?

May 21, 2018

sqrt14-(sqrt2)=color(blue)((7sqrt14-sqrt2)/7

Explanation:

Simplify:

$\sqrt{14} - \frac{\sqrt{2}}{7}$

In order to add or subtract fractions, they must have the same denominator; the least common denominator (LCD). The LCD for this expression is $7$.

Multiply $\sqrt{14}$ by $\frac{7}{7}$ to get an equivalent fraction with $7$ as the denominator. Since $\frac{7}{7} = 1$, the numbers will change, but the value will remain the same.

$\sqrt{14} \times \frac{7}{7} - \frac{\sqrt{2}}{7}$

Simplify $\sqrt{14} \times \frac{7}{7}$ to $\frac{7 \sqrt{14}}{7}$.

$\frac{7 \sqrt{14}}{7} - \frac{\sqrt{2}}{7}$

Combine the numerators.

$\frac{7 \sqrt{14} - \sqrt{2}}{7}$

May 21, 2018

$\sqrt{14} - \frac{\sqrt{2}}{7} = \sqrt{2} \left(\sqrt{7} - \frac{1}{7}\right)$

Explanation:

$\sqrt{14} - \frac{\sqrt{2}}{7}$
$= \sqrt{7} \cdot \sqrt{2} - \frac{\sqrt{2}}{7}$
$= \sqrt{2} \left(\sqrt{7} - \frac{1}{7}\right)$