Solve the Rational Equation for n square root of n+9=1

$\sqrt{n + 9} = 1$

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

${\sqrt{n + 9}}^{2} = 1^{2}$

Simplify each side of the equation.

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{n + 9}$ as ${(n + 9)}^{\frac{1}{2}}$ .

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

Simplify the left side.

Simplify ${({(n + 9)}^{\frac{1}{2}})}^{2}$ .

Multiply the exponents in ${({(n + 9)}^{\frac{1}{2}})}^{2}$ .

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

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

Cancel the common factor of $2$ .

Cancel the common factor.

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

Rewrite the expression.

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

Simplify.

$n + 9 = 1^{2}$

Simplify the right side.

One to any power is one.

$n + 9 = 1$

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

Subtract $9$ from both sides of the equation.

$n = 1 - 9$

Subtract $9$ from $1$ .

$n = - 8$