Solve by Factoring square root of x-6=3

$\sqrt{x} - 6 = 3$

Step 1

Subtract $3$ from both sides of the equation.

$\sqrt{x} - 6 - 3 = 0$

Step 2

Subtract $3$ from $- 6$ .

$\sqrt{x} - 9 = 0$

Step 3

Add $9$ to both sides of the equation.

$\sqrt{x} = 9$

Step 4

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

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

Step 5

Simplify each side of the equation.

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

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

Simplify the left side.

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

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

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

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

Cancel the common factor of $2$ .

Cancel the common factor.

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

Rewrite the expression.

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

Simplify.

$x = 9^{2}$

Simplify the right side.

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

$x = 81$