Solve for x square root of x+3+8=7

$\sqrt{x + 3 + 8} = 7$

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

${\sqrt{x + 3 + 8}}^{2} = 7^{2}$

Simplify each side of the equation.

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{x + 3 + 8}$ as ${(x + 3 + 8)}^{\frac{1}{2}}$ .

${({(x + 3 + 8)}^{\frac{1}{2}})}^{2} = 7^{2}$

Simplify the left side.

Simplify ${({(x + 3 + 8)}^{\frac{1}{2}})}^{2}$ .

Multiply the exponents in ${({(x + 3 + 8)}^{\frac{1}{2}})}^{2}$ .

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

${(x + 3 + 8)}^{\frac{1}{2} \cdot 2} = 7^{2}$

Cancel the common factor of $2$ .

Cancel the common factor.

${(x + 3 + 8)}^{\frac{1}{2} \cdot 2} = 7^{2}$

Rewrite the expression.

${(x + 3 + 8)}^{1} = 7^{2}$

Add $3$ and $8$ .

${(x + 11)}^{1} = 7^{2}$

Simplify.

$x + 11 = 7^{2}$

Simplify the right side.

Raise $7$ to the power of $2$ .

$x + 11 = 49$

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

Subtract $11$ from both sides of the equation.

$x = 49 - 11$

Subtract $11$ from $49$ .

$x = 38$