Basic Math Examples

p \cdot r^{2} = 58.27

$p \cdot r^{2} = 58.27$

Step 1

Divide each term in

p \cdot r^{2} = 58.27

$p \cdot r^{2} = 58.27$ by

p

$p$ and simplify.

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Step 1.1

Divide each term in

p \cdot r^{2} = 58.27

$p \cdot r^{2} = 58.27$ by

p

$p$ .

\frac{p \cdot r^{2}}{p} = \frac{58.27}{p}

$\frac{p \cdot r^{2}}{p} = \frac{58.27}{p}$

Step 1.2

Simplify the left side.

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Step 1.2.1

Cancel the common factor of

p

$p$ .

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Step 1.2.1.1

Cancel the common factor.

$\frac{p \cdot r^{2}}{p} = \frac{58.27}{p}$

Step 1.2.1.2

Divide

$r^{2}$ by

$1$ .

$r^{2} = \frac{58.27}{p}$

Step 2

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

$r = \pm \sqrt{\frac{58.27}{p}}$

Step 3

Simplify

$\pm \sqrt{\frac{58.27}{p}}$ .

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Step 3.1

Rewrite

$\sqrt{\frac{58.27}{p}}$ as

$\frac{\sqrt{58.27}}{\sqrt{p}}$ .

$r = \pm \frac{\sqrt{58.27}}{\sqrt{p}}$

Step 3.2

Multiply

$\frac{\sqrt{58.27}}{\sqrt{p}}$ by

$\frac{\sqrt{p}}{\sqrt{p}}$ .

$r = \pm \frac{\sqrt{58.27}}{\sqrt{p}} \cdot \frac{\sqrt{p}}{\sqrt{p}}$

Step 3.3

Simplify terms.

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Step 3.3.1

Combine and simplify the denominator.

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Step 3.3.1.1

Multiply

$\frac{\sqrt{58.27}}{\sqrt{p}}$ by

$\frac{\sqrt{p}}{\sqrt{p}}$ .

$r = \pm \frac{\sqrt{58.27} \sqrt{p}}{\sqrt{p} \sqrt{p}}$

Step 3.3.1.2

Raise

$\sqrt{p}$ to the power of

$1$ .

$r = \pm \frac{\sqrt{58.27} \sqrt{p}}{{\sqrt{p}}^{1} \sqrt{p}}$

Step 3.3.1.3

Raise

$\sqrt{p}$ to the power of

$1$ .

$r = \pm \frac{\sqrt{58.27} \sqrt{p}}{{\sqrt{p}}^{1} {\sqrt{p}}^{1}}$

Step 3.3.1.4

Use the power rule

$a^{m} a^{n} = a^{m + n}$ to combine exponents.

$r = \pm \frac{\sqrt{58.27} \sqrt{p}}{{\sqrt{p}}^{1 + 1}}$

Step 3.3.1.5

Add

$1$ and

$1$ .

$r = \pm \frac{\sqrt{58.27} \sqrt{p}}{{\sqrt{p}}^{2}}$

Step 3.3.1.6

Rewrite

${\sqrt{p}}^{2}$ as

$p$ .

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Step 3.3.1.6.1

Use

$\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite

$\sqrt{p}$ as

$p^{\frac{1}{2}}$ .

$r = \pm \frac{\sqrt{58.27} \sqrt{p}}{{(p^{\frac{1}{2}})}^{2}}$

Step 3.3.1.6.2

Apply the power rule and multiply exponents,

${(a^{m})}^{n} = a^{m n}$ .

$r = \pm \frac{\sqrt{58.27} \sqrt{p}}{p^{\frac{1}{2} \cdot 2}}$

Step 3.3.1.6.3

Combine

$\frac{1}{2}$ and

$2$ .

$r = \pm \frac{\sqrt{58.27} \sqrt{p}}{p^{\frac{2}{2}}}$

Step 3.3.1.6.4

Cancel the common factor of

$2$ .

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Step 3.3.1.6.4.1

Cancel the common factor.

$r = \pm \frac{\sqrt{58.27} \sqrt{p}}{p^{\frac{2}{2}}}$

Step 3.3.1.6.4.2

Rewrite the expression.

$r = \pm \frac{\sqrt{58.27} \sqrt{p}}{p^{1}}$

Step 3.3.1.6.5

Simplify.

$r = \pm \frac{\sqrt{58.27} \sqrt{p}}{p}$

Step 3.3.2

Combine using the product rule for radicals.

$r = \pm \frac{\sqrt{58.27 p}}{p}$

Step 3.4

Simplify the numerator.

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Step 3.4.1

Rewrite

$58.27 p$ as

${({2.76287511}^{2})}^{2} p$ .

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Step 3.4.1.1

Rewrite

$58.27$ as

${7.63347889}^{2}$ .

$r = \pm \frac{\sqrt{{7.63347889}^{2} p}}{p}$

Step 3.4.1.2

Rewrite

$7.63347889$ as

${2.76287511}^{2}$ .

$r = \pm \frac{\sqrt{{({2.76287511}^{2})}^{2} p}}{p}$

Step 3.4.2

Pull terms out from under the radical.

$r = \pm \frac{{2.76287511}^{2} \sqrt{p}}{p}$

Step 3.4.3

Raise

$2.76287511$ to the power of

$2$ .

$r = \pm \frac{7.63347889 \sqrt{p}}{p}$

Step 4

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

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Step 4.1

First, use the positive value of the

$\pm$ to find the first solution.

$r = \frac{7.63347889 \sqrt{p}}{p}$

Step 4.2

Next, use the negative value of the

$\pm$ to find the second solution.

$r = - \frac{7.63347889 \sqrt{p}}{p}$

Step 4.3

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

$r = \frac{7.63347889 \sqrt{p}}{p}$

$r = - \frac{7.63347889 \sqrt{p}}{p}$

$r = \frac{7.63347889 \sqrt{p}}{p}$

$r = - \frac{7.63347889 \sqrt{p}}{p}$