Algebra Examples

$r = \sqrt{\frac{A}{π}}$

Step 1

Rewrite the equation as $\sqrt{\frac{A}{π}} = r$ .

$\sqrt{\frac{A}{π}} = r$

Step 2

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

${\sqrt{\frac{A}{π}}}^{2} = r^{2}$

Step 3

Simplify each side of the equation.

Tap for more steps...

Step 3.1

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

${({(\frac{A}{π})}^{\frac{1}{2}})}^{2} = r^{2}$

Step 3.2

Simplify the left side.

Tap for more steps...

Step 3.2.1

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

Tap for more steps...

Step 3.2.1.1

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

Tap for more steps...

Step 3.2.1.1.1

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

${(\frac{A}{π})}^{\frac{1}{2} \cdot 2} = r^{2}$

Step 3.2.1.1.2

Cancel the common factor of $2$ .

Tap for more steps...

Step 3.2.1.1.2.1

Cancel the common factor.

${(\frac{A}{π})}^{\frac{1}{2} \cdot 2} = r^{2}$

Step 3.2.1.1.2.2

Rewrite the expression.

${(\frac{A}{π})}^{1} = r^{2}$

Step 3.2.1.2

Simplify.

$\frac{A}{π} = r^{2}$

Step 4

Solve for $A$ .

Tap for more steps...

Step 4.1

Multiply both sides of the equation by $π$ .

$π \frac{A}{π} = π r^{2}$

Step 4.2

Simplify the left side.

Tap for more steps...

Step 4.2.1

Cancel the common factor of $π$ .

Tap for more steps...

Step 4.2.1.1

Cancel the common factor.

$π \frac{A}{π} = π r^{2}$

Step 4.2.1.2

Rewrite the expression.

$A = π r^{2}$