Solve for y 13 = square root of y

$13 = \sqrt{y}$

Rewrite the equation as $\sqrt{y} = 13$ .

$\sqrt{y} = 13$

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

${\sqrt{y}}^{2} = 13^{2}$

Simplify each side of the equation.

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

${(y^{\frac{1}{2}})}^{2} = 13^{2}$

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

$y^{\frac{1}{2} \cdot 2} = 13^{2}$

Cancel the common factor of $2$ .

Cancel the common factor.

$y^{\frac{1}{2} \cdot 2} = 13^{2}$

Rewrite the expression.

$y^{1} = 13^{2}$

Simplify.

$y = 13^{2}$

Simplify the right side.

Raise $13$ to the power of $2$ .

$y = 169$