# How to find the answer for 4sqrtx(2sqrtx+3sqrt7) and simplify it too?

Sep 26, 2017

$8 x + 12 \sqrt{7} \sqrt{x}$

#### Explanation:

First, we distribute parentheses/brackets using: $x \left(y + z\right) = x y + x z$

Therefore,
$4 \sqrt{x} \left(2 \sqrt{x} + 3 \sqrt{7}\right)$ is the same as $4 \sqrt{x} \cdot 2 \sqrt{x} + 4 \sqrt{x} \cdot 3 \sqrt{7}$

$4 \sqrt{x} \cdot 2 \sqrt{x} = 8 x$ because $\sqrt{x} \cdot \sqrt{x} = x$
So, you can just multiply the numbers: $4 \cdot 2 = 8$ and add the $x$.

For $4 \sqrt{x} \cdot 3 \sqrt{7} ,$ you take $4 \cdot 3 = 12$ and you combine $\sqrt{x}$ and $\sqrt{7}$ together.
So, the equation on the right side would be $12 \sqrt{7} \sqrt{x}$.

$8 x + 12 \sqrt{7} \sqrt{x}$