Solve for x square root of x+4 = square root of 3x

$\sqrt{x + 4} = \sqrt{3 x}$

To remove the radical on the left side of the equation, square both sides of the equation.

${\sqrt{x + 4}}^{2} = {\sqrt{3 x}}^{2}$

Simplify each side of the equation.

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{x + 4}$ as ${(x + 4)}^{\frac{1}{2}}$ .

${({(x + 4)}^{\frac{1}{2}})}^{2} = {\sqrt{3 x}}^{2}$

Simplify the left side.

Simplify ${({(x + 4)}^{\frac{1}{2}})}^{2}$ .

Multiply the exponents in ${({(x + 4)}^{\frac{1}{2}})}^{2}$ .

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

${(x + 4)}^{\frac{1}{2} \cdot 2} = {\sqrt{3 x}}^{2}$

Cancel the common factor of $2$ .

Cancel the common factor.

${(x + 4)}^{\frac{1}{2} \cdot 2} = {\sqrt{3 x}}^{2}$

Rewrite the expression.

${(x + 4)}^{1} = {\sqrt{3 x}}^{2}$

Simplify.

$x + 4 = {\sqrt{3 x}}^{2}$

Simplify the right side.

Rewrite ${\sqrt{3 x}}^{2}$ as $3 x$ .

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{3 x}$ as ${(3 x)}^{\frac{1}{2}}$ .

$x + 4 = {({(3 x)}^{\frac{1}{2}})}^{2}$

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

$x + 4 = {(3 x)}^{\frac{1}{2} \cdot 2}$

Combine $\frac{1}{2}$ and $2$ .

$x + 4 = {(3 x)}^{\frac{2}{2}}$

Cancel the common factor of $2$ .

Cancel the common factor.

$x + 4 = {(3 x)}^{\frac{2}{2}}$

Rewrite the expression.

$x + 4 = {(3 x)}^{1}$

Simplify.

$x + 4 = 3 x$

Solve for $x$ .

Move all terms containing $x$ to the left side of the equation.

Subtract $3 x$ from both sides of the equation.

$x + 4 - 3 x = 0$

Subtract $3 x$ from $x$ .

$- 2 x + 4 = 0$

Subtract $4$ from both sides of the equation.

$- 2 x = - 4$

Divide each term in $- 2 x = - 4$ by $- 2$ and simplify.

Divide each term in $- 2 x = - 4$ by $- 2$ .

$\frac{- 2 x}{- 2} = \frac{- 4}{- 2}$

Simplify the left side.

Cancel the common factor of $- 2$ .

Cancel the common factor.

$\frac{- 2 x}{- 2} = \frac{- 4}{- 2}$

Divide $x$ by $1$ .

$x = \frac{- 4}{- 2}$

Simplify the right side.

Divide $- 4$ by $- 2$ .

$x = 2$

Solve for x square root of x+4 = square root of 3x

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