Solve the Rational Equation for n square root of n=9

$\sqrt{n} = 9$

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

${\sqrt{n}}^{2} = 9^{2}$

Simplify each side of the equation.

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

${(n^{\frac{1}{2}})}^{2} = 9^{2}$

Simplify the left side.

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

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

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

$n^{\frac{1}{2} \cdot 2} = 9^{2}$

Cancel the common factor of $2$ .

Cancel the common factor.

$n^{\frac{1}{2} \cdot 2} = 9^{2}$

Rewrite the expression.

$n^{1} = 9^{2}$

Simplify.

$n = 9^{2}$

Simplify the right side.

Raise $9$ to the power of $2$ .

$n = 81$