Solve for x y = square root of ax

$y = \sqrt{a x}$

Step 1

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

$\sqrt{a x} = y$

Step 2

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

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

Step 3

Simplify each side of the equation.

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

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

Simplify the left side.

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

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

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

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

Cancel the common factor of $2$ .

Cancel the common factor.

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

Rewrite the expression.

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

Simplify.

$a x = y^{2}$

Step 4

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

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

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

Simplify the left side.

Cancel the common factor of $a$ .

Cancel the common factor.

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

Divide $x$ by $1$ .

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