Solve for d a=pi(d^2)/4

$a = π \frac{d^{2}}{4}$

Rewrite the equation as $π (\frac{d^{2}}{4}) = a$ .

$π (\frac{d^{2}}{4}) = a$

Combine $π$ and $\frac{d^{2}}{4}$ .

$\frac{π d^{2}}{4} = a$

Divide each term in $\frac{π d^{2}}{4} = a$ by $π$ and simplify.

Divide each term in $\frac{π d^{2}}{4} = a$ by $π$ .

$\frac{\frac{π d^{2}}{4}}{π} = \frac{a}{π}$

Simplify the left side.

Multiply the numerator by the reciprocal of the denominator.

$\frac{π d^{2}}{4} \cdot \frac{1}{π} = \frac{a}{π}$

Combine.

$\frac{π d^{2} \cdot 1}{4 π} = \frac{a}{π}$

Cancel the common factor of $π$ .

Cancel the common factor.

$\frac{π d^{2} \cdot 1}{4 π} = \frac{a}{π}$

Rewrite the expression.

$\frac{d^{2} \cdot 1}{4} = \frac{a}{π}$

Multiply $d^{2}$ by $1$ .

$\frac{d^{2}}{4} = \frac{a}{π}$

Multiply both sides of the equation by $4$ .

$4 \frac{d^{2}}{4} = 4 \frac{a}{π}$

Simplify both sides of the equation.

Simplify the left side.

Cancel the common factor of $4$ .

Cancel the common factor.

$4 \frac{d^{2}}{4} = 4 \frac{a}{π}$

Rewrite the expression.

$d^{2} = 4 \frac{a}{π}$

Simplify the right side.

Combine $4$ and $\frac{a}{π}$ .

$d^{2} = \frac{4 a}{π}$

Take the square root of both sides of the equation to eliminate the exponent on the left side.

$d = \pm \sqrt{\frac{4 a}{π}}$

Simplify $\pm \sqrt{\frac{4 a}{π}}$ .

Rewrite $\sqrt{\frac{4 a}{π}}$ as $\frac{\sqrt{4 a}}{\sqrt{π}}$ .

$d = \pm \frac{\sqrt{4 a}}{\sqrt{π}}$

Simplify the numerator.

Rewrite $4$ as $2^{2}$ .

$d = \pm \frac{\sqrt{2^{2} a}}{\sqrt{π}}$

Pull terms out from under the radical.

$d = \pm \frac{2 \sqrt{a}}{\sqrt{π}}$

Multiply $\frac{2 \sqrt{a}}{\sqrt{π}}$ by $\frac{\sqrt{π}}{\sqrt{π}}$ .

$d = \pm \frac{2 \sqrt{a}}{\sqrt{π}} \cdot \frac{\sqrt{π}}{\sqrt{π}}$

Combine and simplify the denominator.

Multiply $\frac{2 \sqrt{a}}{\sqrt{π}}$ by $\frac{\sqrt{π}}{\sqrt{π}}$ .

$d = \pm \frac{2 \sqrt{a} \sqrt{π}}{\sqrt{π} \sqrt{π}}$

Raise $\sqrt{π}$ to the power of $1$ .

$d = \pm \frac{2 \sqrt{a} \sqrt{π}}{{\sqrt{π}}^{1} \sqrt{π}}$

Raise $\sqrt{π}$ to the power of $1$ .

$d = \pm \frac{2 \sqrt{a} \sqrt{π}}{{\sqrt{π}}^{1} {\sqrt{π}}^{1}}$

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$d = \pm \frac{2 \sqrt{a} \sqrt{π}}{{\sqrt{π}}^{1 + 1}}$

Add $1$ and $1$ .

$d = \pm \frac{2 \sqrt{a} \sqrt{π}}{{\sqrt{π}}^{2}}$

Rewrite ${\sqrt{π}}^{2}$ as $π$ .

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

$d = \pm \frac{2 \sqrt{a} \sqrt{π}}{{(π^{\frac{1}{2}})}^{2}}$

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

$d = \pm \frac{2 \sqrt{a} \sqrt{π}}{π^{\frac{1}{2} \cdot 2}}$

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

$d = \pm \frac{2 \sqrt{a} \sqrt{π}}{π^{\frac{2}{2}}}$

Cancel the common factor of $2$ .

Cancel the common factor.

$d = \pm \frac{2 \sqrt{a} \sqrt{π}}{π^{\frac{2}{2}}}$

Rewrite the expression.

$d = \pm \frac{2 \sqrt{a} \sqrt{π}}{π^{1}}$

Simplify.

$d = \pm \frac{2 \sqrt{a} \sqrt{π}}{π}$

Combine using the product rule for radicals.

$d = \pm \frac{2 \sqrt{π a}}{π}$

The complete solution is the result of both the positive and negative portions of the solution.

First, use the positive value of the $\pm$ to find the first solution.

$d = \frac{2 \sqrt{π a}}{π}$

Next, use the negative value of the $\pm$ to find the second solution.

$d = - \frac{2 \sqrt{π a}}{π}$

The complete solution is the result of both the positive and negative portions of the solution.

$d = \frac{2 \sqrt{π a}}{π}$

$d = - \frac{2 \sqrt{π a}}{π}$

$d = \frac{2 \sqrt{π a}}{π}$

$d = - \frac{2 \sqrt{π a}}{π}$

Solve for d a=pi(d^2)/4

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