Solve the Rational Equation for y square root of y=3 square root of 5

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

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

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

Simplify each side of the equation.

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

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

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

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

Cancel the common factor of $2$ .

Cancel the common factor.

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

Rewrite the expression.

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

Simplify.

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

Simplify the right side.

Simplify ${(3 \sqrt{5})}^{2}$ .

Simplify the expression.

Apply the product rule to $3 \sqrt{5}$ .

$y = 3^{2} {\sqrt{5}}^{2}$

Raise $3$ to the power of $2$ .

$y = 9 {\sqrt{5}}^{2}$

Rewrite ${\sqrt{5}}^{2}$ as $5$ .

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{5}$ as $5^{\frac{1}{2}}$ .

$y = 9 {(5^{\frac{1}{2}})}^{2}$

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

$y = 9 \cdot 5^{\frac{1}{2} \cdot 2}$

Combine $\frac{1}{2}$ and $2$ .

$y = 9 \cdot 5^{\frac{2}{2}}$

Cancel the common factor of $2$ .

Cancel the common factor.

$y = 9 \cdot 5^{\frac{2}{2}}$

Rewrite the expression.

$y = 9 \cdot 5^{1}$

Evaluate the exponent.

$y = 9 \cdot 5$

Multiply $9$ by $5$ .

$y = 45$