Evaluate 3+ square root of x+2=11

$3 + \sqrt{x + 2} = 11$

Move all terms not containing $\sqrt{x + 2}$ to the right side of the equation.

Subtract $3$ from both sides of the equation.

$\sqrt{x + 2} = 11 - 3$

Subtract $3$ from $11$ .

$\sqrt{x + 2} = 8$

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

${\sqrt{x + 2}}^{2} = 8^{2}$

Simplify each side of the equation.

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

${({(x + 2)}^{\frac{1}{2}})}^{2} = 8^{2}$

Simplify the left side.

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

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

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

${(x + 2)}^{\frac{1}{2} \cdot 2} = 8^{2}$

Cancel the common factor of $2$ .

Cancel the common factor.

${(x + 2)}^{\frac{1}{2} \cdot 2} = 8^{2}$

Rewrite the expression.

${(x + 2)}^{1} = 8^{2}$

Simplify.

$x + 2 = 8^{2}$

Simplify the right side.

Raise $8$ to the power of $2$ .

$x + 2 = 64$

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

Subtract $2$ from both sides of the equation.

$x = 64 - 2$

Subtract $2$ from $64$ .

$x = 62$