# How do you solve sqrt(4x)=64 and check the solution?

Jul 29, 2017

See two solution processes below:

#### Explanation:

Process 1
First, square both sides of the equation to eliminate the radical while keeping the equation balanced:

${\left(\sqrt{4 x}\right)}^{2} = {64}^{2}$

$4 x = 4096$

Now, divide each side of the equation by $\textcolor{red}{4}$ to solve for $x$ while keeping the equation balanced:

$\frac{4 x}{\textcolor{red}{4}} = \frac{4096}{\textcolor{red}{4}}$

$\frac{\textcolor{red}{\cancel{\textcolor{b l a c k}{4}}} x}{\cancel{\textcolor{red}{4}}} = 1024$

$x = 1024$

Process 2
First, simplify the radical on the left using this rule:

$\sqrt{\textcolor{red}{a} \cdot \textcolor{b l u e}{b}} = \sqrt{\textcolor{red}{a}} \cdot \sqrt{\textcolor{b l u e}{b}}$

$\sqrt{4 x} = 64$

$\sqrt{\textcolor{red}{4} \cdot \textcolor{b l u e}{x}} = 64$

$\sqrt{\textcolor{red}{4}} \sqrt{\textcolor{b l u e}{x}} = 64$

$2 \sqrt{\textcolor{b l u e}{x}} = 64$

Now, divide each side of the equation by $\textcolor{red}{2}$ to isolate the $x$ term while keeping the equation balanced:

$\frac{2 \sqrt{\textcolor{b l u e}{x}}}{\textcolor{red}{2}} = \frac{64}{\textcolor{red}{2}}$

$\frac{\textcolor{red}{\cancel{\textcolor{b l a c k}{2}}} \sqrt{\textcolor{b l u e}{x}}}{\cancel{\textcolor{red}{2}}} = 32$

$\sqrt{\textcolor{b l u e}{x}} = 32$

Now, square both sides of the equation to eliminate the radical and solve for $x$ while keeping the equation balanced:

${\left(\sqrt{\textcolor{b l u e}{x}}\right)}^{2} = {32}^{2}$

$x = 1024$