Solve for m square root of m+6=9

$\sqrt{m + 6} = 9$

Step 1

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

${\sqrt{m + 6}}^{2} = 9^{2}$

Step 2

Simplify each side of the equation.

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{m + 6}$ as ${(m + 6)}^{\frac{1}{2}}$ .

${({(m + 6)}^{\frac{1}{2}})}^{2} = 9^{2}$

Simplify the left side.

Simplify ${({(m + 6)}^{\frac{1}{2}})}^{2}$ .

Multiply the exponents in ${({(m + 6)}^{\frac{1}{2}})}^{2}$ .

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

${(m + 6)}^{\frac{1}{2} \cdot 2} = 9^{2}$

Cancel the common factor of $2$ .

Cancel the common factor.

${(m + 6)}^{\frac{1}{2} \cdot 2} = 9^{2}$

Rewrite the expression.

${(m + 6)}^{1} = 9^{2}$

Simplify.

$m + 6 = 9^{2}$

Simplify the right side.

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

$m + 6 = 81$

Step 3

Move all terms not containing $m$ to the right side of the equation.

Subtract $6$ from both sides of the equation.

$m = 81 - 6$

Subtract $6$ from $81$ .

$m = 75$