Solve for k square root of k+2-9=0

$\sqrt{k + 2} - 9 = 0$

Add $9$ to both sides of the equation.

$\sqrt{k + 2} = 9$

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

${\sqrt{k + 2}}^{2} = 9^{2}$

Simplify each side of the equation.

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

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

Simplify the left side.

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

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

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

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

Cancel the common factor of $2$ .

Cancel the common factor.

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

Rewrite the expression.

${(k + 2)}^{1} = 9^{2}$

Simplify.

$k + 2 = 9^{2}$

Simplify the right side.

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

$k + 2 = 81$

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

Subtract $2$ from both sides of the equation.

$k = 81 - 2$

Subtract $2$ from $81$ .

$k = 79$