Solve for y square root of y-3=-5

$\sqrt{y - 3} = - 5$

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

${\sqrt{y - 3}}^{2} = {(- 5)}^{2}$

Simplify each side of the equation.

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

${({(y - 3)}^{\frac{1}{2}})}^{2} = {(- 5)}^{2}$

Simplify the left side.

Simplify ${({(y - 3)}^{\frac{1}{2}})}^{2}$ .

Multiply the exponents in ${({(y - 3)}^{\frac{1}{2}})}^{2}$ .

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

${(y - 3)}^{\frac{1}{2} \cdot 2} = {(- 5)}^{2}$

Cancel the common factor of $2$ .

Cancel the common factor.

${(y - 3)}^{\frac{1}{2} \cdot 2} = {(- 5)}^{2}$

Rewrite the expression.

${(y - 3)}^{1} = {(- 5)}^{2}$

Simplify.

$y - 3 = {(- 5)}^{2}$

Simplify the right side.

Raise $- 5$ to the power of $2$ .

$y - 3 = 25$

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

Add $3$ to both sides of the equation.

$y = 25 + 3$

Add $25$ and $3$ .

$y = 28$

Exclude the solutions that do not make $\sqrt{y - 3} = - 5$ true.

$No solution$