Solve for y 7 = square root of y+2

$7 = \sqrt{y} + 2$

Rewrite the equation as $\sqrt{y} + 2 = 7$ .

$\sqrt{y} + 2 = 7$

Move all terms not containing $\sqrt{y}$ to the right side of the equation.

Subtract $2$ from both sides of the equation.

$\sqrt{y} = 7 - 2$

Subtract $2$ from $7$ .

$\sqrt{y} = 5$

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

${\sqrt{y}}^{2} = 5^{2}$

Simplify each side of the equation.

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

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

Simplify the left side.

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

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

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

$y^{\frac{1}{2} \cdot 2} = 5^{2}$

Cancel the common factor of $2$ .

Cancel the common factor.

$y^{\frac{1}{2} \cdot 2} = 5^{2}$

Rewrite the expression.

$y^{1} = 5^{2}$

Simplify.

$y = 5^{2}$

Simplify the right side.

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

$y = 25$