Solve for y square root of y-7=0

$\sqrt{y} - 7 = 0$

Add $7$ to both sides of the equation.

$\sqrt{y} = 7$

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

${\sqrt{y}}^{2} = 7^{2}$

Simplify each side of the equation.

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

${(y^{\frac{1}{2}})}^{2} = 7^{2}$

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, ${(a^{m})}^{n} = a^{m n}$ .

$y^{\frac{1}{2} \cdot 2} = 7^{2}$

Cancel the common factor of $2$ .

Cancel the common factor.

$y^{\frac{1}{2} \cdot 2} = 7^{2}$

Rewrite the expression.

$y^{1} = 7^{2}$

Simplify.

$y = 7^{2}$

Simplify the right side.

Raise $7$ to the power of $2$ .

$y = 49$