Solve for y square root of y-8=-1

$\sqrt{y - 8} = - 1$

Step 1

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

${\sqrt{y - 8}}^{2} = {(- 1)}^{2}$

Step 2

Simplify each side of the equation.

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

${({(y - 8)}^{\frac{1}{2}})}^{2} = {(- 1)}^{2}$

Simplify the left side.

Simplify ${({(y - 8)}^{\frac{1}{2}})}^{2}$ .

Multiply the exponents in ${({(y - 8)}^{\frac{1}{2}})}^{2}$ .

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

${(y - 8)}^{\frac{1}{2} \cdot 2} = {(- 1)}^{2}$

Cancel the common factor of $2$ .

Cancel the common factor.

${(y - 8)}^{\frac{1}{2} \cdot 2} = {(- 1)}^{2}$

Rewrite the expression.

${(y - 8)}^{1} = {(- 1)}^{2}$

Simplify.

$y - 8 = {(- 1)}^{2}$

Simplify the right side.

Raise $- 1$ to the power of $2$ .

$y - 8 = 1$

Step 3

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

Add $8$ to both sides of the equation.

$y = 1 + 8$

Add $1$ and $8$ .

$y = 9$

Step 4

Exclude the solutions that do not make $\sqrt{y - 8} = - 1$ true.

$No solution$