# How do you simplify sqrt(7x)(sqrt x-7sqrt 7)?

Feb 4, 2016

$\sqrt{7} x - 49 \sqrt{x}$

#### Explanation:

First of all, expand by multiplying $\sqrt{7 x} \cdot \sqrt{x}$ and $\sqrt{7 x} \cdot 7 \sqrt{7}$ respectively:

$\sqrt{7 x} \left(\sqrt{x} - 7 \sqrt{7}\right) = \sqrt{7 x} \cdot \sqrt{x} - \sqrt{7 x} \cdot 7 \sqrt{7}$

... you can express $\sqrt{7 x}$ as $\sqrt{7} \cdot \sqrt{x}$...

$= \sqrt{7} \cdot \textcolor{b l u e}{\sqrt{x} \cdot \sqrt{x}} - \textcolor{\mathmr{and} a n \ge}{\sqrt{7}} \cdot \sqrt{x} \cdot 7 \cdot \textcolor{\mathmr{and} a n \ge}{\sqrt{7}}$

$= \sqrt{7} \cdot \textcolor{b l u e}{{\left(\sqrt{x}\right)}^{2}} - \textcolor{\mathmr{and} a n \ge}{{\left(\sqrt{7}\right)}^{2}} \cdot \sqrt{x} \cdot 7$

... the operations squaring and taking the square root "eliminate each other"...

$= \sqrt{7} \cdot x - 7 \cdot \sqrt{x} \cdot 7$

$= \sqrt{7} x - 49 \sqrt{x}$

Hope that this helped!