Solve for x y=a square root of x

$y = a \sqrt{x}$

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

$a \sqrt{x} = y$

Divide each term in $a \sqrt{x} = y$ by $a$ and simplify.

Divide each term in $a \sqrt{x} = y$ by $a$ .

$\frac{a \sqrt{x}}{a} = \frac{y}{a}$

Simplify the left side.

Cancel the common factor of $a$ .

Cancel the common factor.

$\frac{a \sqrt{x}}{a} = \frac{y}{a}$

Divide $\sqrt{x}$ by $1$ .

$\sqrt{x} = \frac{y}{a}$

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

${\sqrt{x}}^{2} = {(\frac{y}{a})}^{2}$

Simplify each side of the equation.

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

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

Simplify the left side.

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

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

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

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

Cancel the common factor of $2$ .

Cancel the common factor.

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

Rewrite the expression.

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

Simplify.

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

Simplify the right side.

Apply the product rule to $\frac{y}{a}$ .

$x = \frac{y^{2}}{a^{2}}$