Solve for y x=( square root of 5y)/15

$x = \frac{\sqrt{5 y}}{15}$

Step 1

Rewrite the equation as $\frac{\sqrt{5 y}}{15} = x$ .

$\frac{\sqrt{5 y}}{15} = x$

Step 2

Multiply both sides by $15$ .

$\frac{\sqrt{5 y}}{15} \cdot 15 = x \cdot 15$

Step 3

Simplify.

Simplify the left side.

Cancel the common factor of $15$ .

Cancel the common factor.

$\frac{\sqrt{5 y}}{15} \cdot 15 = x \cdot 15$

Rewrite the expression.

$\sqrt{5 y} = x \cdot 15$

Simplify the right side.

Move $15$ to the left of $x$ .

$\sqrt{5 y} = 15 x$

Step 4

Solve for $y$ .

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

${\sqrt{5 y}}^{2} = {(15 x)}^{2}$

Simplify each side of the equation.

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

${({(5 y)}^{\frac{1}{2}})}^{2} = {(15 x)}^{2}$

Simplify the left side.

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

Multiply the exponents in ${({(5 y)}^{\frac{1}{2}})}^{2}$ .

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

${(5 y)}^{\frac{1}{2} \cdot 2} = {(15 x)}^{2}$

Cancel the common factor of $2$ .

Cancel the common factor.

${(5 y)}^{\frac{1}{2} \cdot 2} = {(15 x)}^{2}$

Rewrite the expression.

${(5 y)}^{1} = {(15 x)}^{2}$

Simplify.

$5 y = {(15 x)}^{2}$

Simplify the right side.

Simplify ${(15 x)}^{2}$ .

Apply the product rule to $15 x$ .

$5 y = 15^{2} x^{2}$

Raise $15$ to the power of $2$ .

$5 y = 225 x^{2}$

Divide each term in $5 y = 225 x^{2}$ by $5$ and simplify.

Divide each term in $5 y = 225 x^{2}$ by $5$ .

$\frac{5 y}{5} = \frac{225 x^{2}}{5}$

Simplify the left side.

Cancel the common factor of $5$ .

Cancel the common factor.

$\frac{5 y}{5} = \frac{225 x^{2}}{5}$

Divide $y$ by $1$ .

$y = \frac{225 x^{2}}{5}$

Simplify the right side.

Cancel the common factor of $225$ and $5$ .

Factor $5$ out of $225 x^{2}$ .

$y = \frac{5 (45 x^{2})}{5}$

Cancel the common factors.

Factor $5$ out of $5$ .

$y = \frac{5 (45 x^{2})}{5 (1)}$

Cancel the common factor.

$y = \frac{5 (45 x^{2})}{5 \cdot 1}$

Rewrite the expression.

$y = \frac{45 x^{2}}{1}$

Divide $45 x^{2}$ by $1$ .

$y = 45 x^{2}$

Solve for y x=( square root of 5y)/15

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