Solve the Rational Equation for h square root of 3h=3

$\sqrt{3 h} = 3$

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

${\sqrt{3 h}}^{2} = 3^{2}$

Simplify each side of the equation.

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

${({(3 h)}^{\frac{1}{2}})}^{2} = 3^{2}$

Simplify the left side.

Simplify ${({(3 h)}^{\frac{1}{2}})}^{2}$ .

Multiply the exponents in ${({(3 h)}^{\frac{1}{2}})}^{2}$ .

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

${(3 h)}^{\frac{1}{2} \cdot 2} = 3^{2}$

Cancel the common factor of $2$ .

Cancel the common factor.

${(3 h)}^{\frac{1}{2} \cdot 2} = 3^{2}$

Rewrite the expression.

${(3 h)}^{1} = 3^{2}$

Simplify.

$3 h = 3^{2}$

Simplify the right side.

Raise $3$ to the power of $2$ .

$3 h = 9$

Divide each term in $3 h = 9$ by $3$ and simplify.

Divide each term in $3 h = 9$ by $3$ .

$\frac{3 h}{3} = \frac{9}{3}$

Simplify the left side.

Cancel the common factor of $3$ .

Cancel the common factor.

$\frac{3 h}{3} = \frac{9}{3}$

Divide $h$ by $1$ .

$h = \frac{9}{3}$

Simplify the right side.

Divide $9$ by $3$ .

$h = 3$