Solve by Factoring square root of 9=9^(1/2)

$\sqrt{9} = 9^{\frac{1}{2}}$

Subtract $9^{\frac{1}{2}}$ from both sides of the equation.

$\sqrt{9} - 9^{\frac{1}{2}} = 0$

Simplify $\sqrt{9} - 9^{\frac{1}{2}}$ .

Simplify each term.

Rewrite $9$ as $3^{2}$ .

$\sqrt{3^{2}} - 9^{\frac{1}{2}} = 0$

Pull terms out from under the radical, assuming positive real numbers.

$3 - 9^{\frac{1}{2}} = 0$

Rewrite $9$ as $3^{2}$ .

$3 - {(3^{2})}^{\frac{1}{2}} = 0$

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

$3 - 3^{2 (\frac{1}{2})} = 0$

Cancel the common factor of $2$ .

Cancel the common factor.

$3 - 3^{2 (\frac{1}{2})} = 0$

Rewrite the expression.

$3 - 3^{1} = 0$

Evaluate the exponent.

$3 - 1 \cdot 3 = 0$

Multiply $- 1$ by $3$ .

$3 - 3 = 0$

Subtract $3$ from $3$ .

$0 = 0$

Since $0 = 0$ , the equation will always be true.

Always true