Solve for n square root of n+2-4=0

$\sqrt{n + 2} - 4 = 0$

Step 1

Add $4$ to both sides of the equation.

$\sqrt{n + 2} = 4$

Step 2

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

${\sqrt{n + 2}}^{2} = 4^{2}$

Step 3

Simplify each side of the equation.

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

${({(n + 2)}^{\frac{1}{2}})}^{2} = 4^{2}$

Simplify the left side.

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

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

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

${(n + 2)}^{\frac{1}{2} \cdot 2} = 4^{2}$

Cancel the common factor of $2$ .

Cancel the common factor.

${(n + 2)}^{\frac{1}{2} \cdot 2} = 4^{2}$

Rewrite the expression.

${(n + 2)}^{1} = 4^{2}$

Simplify.

$n + 2 = 4^{2}$

Simplify the right side.

Raise $4$ to the power of $2$ .

$n + 2 = 16$

Step 4

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

Subtract $2$ from both sides of the equation.

$n = 16 - 2$

Subtract $2$ from $16$ .

$n = 14$