Solve for a r = square root of a/3

$r = \sqrt{\frac{a}{3}}$

Step 1

Rewrite the equation as $\sqrt{\frac{a}{3}} = r$ .

$\sqrt{\frac{a}{3}} = r$

Step 2

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

${\sqrt{\frac{a}{3}}}^{2} = r^{2}$

Step 3

Simplify each side of the equation.

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

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

Simplify the left side.

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

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

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

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

Cancel the common factor of $2$ .

Cancel the common factor.

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

Rewrite the expression.

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

Simplify.

$\frac{a}{3} = r^{2}$

Step 4

Solve for $a$ .

Multiply both sides of the equation by $3$ .

$3 \frac{a}{3} = 3 r^{2}$

Simplify the left side.

Cancel the common factor of $3$ .

Cancel the common factor.

$3 \frac{a}{3} = 3 r^{2}$

Rewrite the expression.

$a = 3 r^{2}$