Basic Math Examples

$300 = p r^{2} \cdot 6$

Step 1

Rewrite the equation as $p r^{2} \cdot 6 = 300$ .

$p r^{2} \cdot 6 = 300$

Step 2

Divide each term in $p r^{2} \cdot 6 = 300$ by $p \cdot 6$ and simplify.

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Step 2.1

Divide each term in $p r^{2} \cdot 6 = 300$ by $p \cdot 6$ .

$\frac{p r^{2} \cdot 6}{p \cdot 6} = \frac{300}{p \cdot 6}$

Step 2.2

Simplify the left side.

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Step 2.2.1

Cancel the common factor of $p$ .

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Step 2.2.1.1

Cancel the common factor.

$\frac{p r^{2} \cdot 6}{p \cdot 6} = \frac{300}{p \cdot 6}$

Step 2.2.1.2

Rewrite the expression.

$\frac{r^{2} \cdot 6}{6} = \frac{300}{p \cdot 6}$

Step 2.2.2

Cancel the common factor of $6$ .

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Step 2.2.2.1

Cancel the common factor.

$\frac{r^{2} \cdot 6}{6} = \frac{300}{p \cdot 6}$

Step 2.2.2.2

Divide $r^{2}$ by $1$ .

$r^{2} = \frac{300}{p \cdot 6}$

Step 2.3

Simplify the right side.

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Step 2.3.1

Cancel the common factor of $300$ and $6$ .

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Step 2.3.1.1

Factor $6$ out of $300$ .

$r^{2} = \frac{6 \cdot 50}{p \cdot 6}$

Step 2.3.1.2

Cancel the common factors.

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Step 2.3.1.2.1

Factor $6$ out of $p \cdot 6$ .

$r^{2} = \frac{6 \cdot 50}{6 \cdot p}$

Step 2.3.1.2.2

Cancel the common factor.

$r^{2} = \frac{6 \cdot 50}{6 \cdot p}$

Step 2.3.1.2.3

Rewrite the expression.

$r^{2} = \frac{50}{p}$

Step 3

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

$r = \pm \sqrt{\frac{50}{p}}$

Step 4

Simplify $\pm \sqrt{\frac{50}{p}}$ .

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Step 4.1

Rewrite $\sqrt{\frac{50}{p}}$ as $\frac{\sqrt{50}}{\sqrt{p}}$ .

$r = \pm \frac{\sqrt{50}}{\sqrt{p}}$

Step 4.2

Simplify the numerator.

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Step 4.2.1

Rewrite $50$ as $5^{2} \cdot 2$ .

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Step 4.2.1.1

Factor $25$ out of $50$ .

$r = \pm \frac{\sqrt{25 (2)}}{\sqrt{p}}$

Step 4.2.1.2

Rewrite $25$ as $5^{2}$ .

$r = \pm \frac{\sqrt{5^{2} \cdot 2}}{\sqrt{p}}$

Step 4.2.2

Pull terms out from under the radical.

$r = \pm \frac{5 \sqrt{2}}{\sqrt{p}}$

Step 4.3

Multiply $\frac{5 \sqrt{2}}{\sqrt{p}}$ by $\frac{\sqrt{p}}{\sqrt{p}}$ .

$r = \pm \frac{5 \sqrt{2}}{\sqrt{p}} \cdot \frac{\sqrt{p}}{\sqrt{p}}$

Step 4.4

Combine and simplify the denominator.

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Step 4.4.1

Multiply $\frac{5 \sqrt{2}}{\sqrt{p}}$ by $\frac{\sqrt{p}}{\sqrt{p}}$ .

$r = \pm \frac{5 \sqrt{2} \sqrt{p}}{\sqrt{p} \sqrt{p}}$

Step 4.4.2

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

$r = \pm \frac{5 \sqrt{2} \sqrt{p}}{{\sqrt{p}}^{1} \sqrt{p}}$

Step 4.4.3

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

$r = \pm \frac{5 \sqrt{2} \sqrt{p}}{{\sqrt{p}}^{1} {\sqrt{p}}^{1}}$

Step 4.4.4

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

$r = \pm \frac{5 \sqrt{2} \sqrt{p}}{{\sqrt{p}}^{1 + 1}}$

Step 4.4.5

Add $1$ and $1$ .

$r = \pm \frac{5 \sqrt{2} \sqrt{p}}{{\sqrt{p}}^{2}}$

Step 4.4.6

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

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Step 4.4.6.1

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

$r = \pm \frac{5 \sqrt{2} \sqrt{p}}{{(p^{\frac{1}{2}})}^{2}}$

Step 4.4.6.2

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

$r = \pm \frac{5 \sqrt{2} \sqrt{p}}{p^{\frac{1}{2} \cdot 2}}$

Step 4.4.6.3

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

$r = \pm \frac{5 \sqrt{2} \sqrt{p}}{p^{\frac{2}{2}}}$

Step 4.4.6.4

Cancel the common factor of $2$ .

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Step 4.4.6.4.1

Cancel the common factor.

$r = \pm \frac{5 \sqrt{2} \sqrt{p}}{p^{\frac{2}{2}}}$

Step 4.4.6.4.2

Rewrite the expression.

$r = \pm \frac{5 \sqrt{2} \sqrt{p}}{p^{1}}$

Step 4.4.6.5

Simplify.

$r = \pm \frac{5 \sqrt{2} \sqrt{p}}{p}$

Step 4.5

Combine using the product rule for radicals.

$r = \pm \frac{5 \sqrt{p \cdot 2}}{p}$

Step 4.6

Move $2$ to the left of $p$ .

$r = \pm \frac{5 \sqrt{2 p}}{p}$

Step 5

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

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Step 5.1

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

$r = \frac{5 \sqrt{2 p}}{p}$

Step 5.2

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

$r = - \frac{5 \sqrt{2 p}}{p}$

Step 5.3

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

$r = \frac{5 \sqrt{2 p}}{p}$

$r = - \frac{5 \sqrt{2 p}}{p}$

$r = \frac{5 \sqrt{2 p}}{p}$

$r = - \frac{5 \sqrt{2 p}}{p}$