Solve by Factoring 4 = square root of m-8

$4 = \sqrt{m} - 8$

Step 1

Move all the expressions to the left side of the equation.

Subtract $\sqrt{m}$ from both sides of the equation.

$4 - \sqrt{m} = - 8$

Add $8$ to both sides of the equation.

$4 - \sqrt{m} + 8 = 0$

Step 2

Add $4$ and $8$ .

$12 - \sqrt{m} = 0$

Step 3

Subtract $12$ from both sides of the equation.

$- \sqrt{m} = - 12$

Step 4

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

${(- \sqrt{m})}^{2} = {(- 12)}^{2}$

Step 5

Simplify each side of the equation.

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

${(- m^{\frac{1}{2}})}^{2} = {(- 12)}^{2}$

Simplify the left side.

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

Apply the product rule to $- m^{\frac{1}{2}}$ .

${(- 1)}^{2} {(m^{\frac{1}{2}})}^{2} = {(- 12)}^{2}$

Raise $- 1$ to the power of $2$ .

$1 {(m^{\frac{1}{2}})}^{2} = {(- 12)}^{2}$

Multiply ${(m^{\frac{1}{2}})}^{2}$ by $1$ .

${(m^{\frac{1}{2}})}^{2} = {(- 12)}^{2}$

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

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

$m^{\frac{1}{2} \cdot 2} = {(- 12)}^{2}$

Cancel the common factor of $2$ .

Cancel the common factor.

$m^{\frac{1}{2} \cdot 2} = {(- 12)}^{2}$

Rewrite the expression.

$m^{1} = {(- 12)}^{2}$

Simplify.

$m = {(- 12)}^{2}$

Simplify the right side.

Raise $- 12$ to the power of $2$ .

$m = 144$