Basic Math Examples

$\sqrt{\frac{\frac{3000 \cdot 4}{300}}{p}}$

Step 1

Reduce the expression by cancelling the common factors.

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Step 1.1

Reduce the expression $\frac{3000 \cdot 4}{300}$ by cancelling the common factors.

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Step 1.1.1

Factor $300$ out of $3000 \cdot 4$ .

$\sqrt{\frac{\frac{300 (10 \cdot 4)}{300}}{p}}$

Step 1.1.2

Factor $300$ out of $300$ .

$\sqrt{\frac{\frac{300 (10 \cdot 4)}{300 (1)}}{p}}$

Step 1.1.3

Cancel the common factor.

$\sqrt{\frac{\frac{300 (10 \cdot 4)}{300 \cdot 1}}{p}}$

Step 1.1.4

Rewrite the expression.

$\sqrt{\frac{\frac{10 \cdot 4}{1}}{p}}$

Step 1.2

Divide $10 \cdot 4$ by $1$ .

$\sqrt{\frac{10 \cdot 4}{p}}$

Step 2

Multiply $10$ by $4$ .

$\sqrt{\frac{40}{p}}$

Step 3

Rewrite $\sqrt{\frac{40}{p}}$ as $\frac{\sqrt{40}}{\sqrt{p}}$ .

$\frac{\sqrt{40}}{\sqrt{p}}$

Step 4

Simplify the numerator.

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Step 4.1

Rewrite $40$ as $2^{2} \cdot 10$ .

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Step 4.1.1

Factor $4$ out of $40$ .

$\frac{\sqrt{4 (10)}}{\sqrt{p}}$

Step 4.1.2

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

$\frac{\sqrt{2^{2} \cdot 10}}{\sqrt{p}}$

Step 4.2

Pull terms out from under the radical.

$\frac{2 \sqrt{10}}{\sqrt{p}}$

Step 5

Multiply $\frac{2 \sqrt{10}}{\sqrt{p}}$ by $\frac{\sqrt{p}}{\sqrt{p}}$ .

$\frac{2 \sqrt{10}}{\sqrt{p}} \cdot \frac{\sqrt{p}}{\sqrt{p}}$

Step 6

Combine and simplify the denominator.

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Step 6.1

Multiply $\frac{2 \sqrt{10}}{\sqrt{p}}$ by $\frac{\sqrt{p}}{\sqrt{p}}$ .

$\frac{2 \sqrt{10} \sqrt{p}}{\sqrt{p} \sqrt{p}}$

Step 6.2

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

$\frac{2 \sqrt{10} \sqrt{p}}{{\sqrt{p}}^{1} \sqrt{p}}$

Step 6.3

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

$\frac{2 \sqrt{10} \sqrt{p}}{{\sqrt{p}}^{1} {\sqrt{p}}^{1}}$

Step 6.4

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

$\frac{2 \sqrt{10} \sqrt{p}}{{\sqrt{p}}^{1 + 1}}$

Step 6.5

Add $1$ and $1$ .

$\frac{2 \sqrt{10} \sqrt{p}}{{\sqrt{p}}^{2}}$

Step 6.6

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

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Step 6.6.1

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

$\frac{2 \sqrt{10} \sqrt{p}}{{(p^{\frac{1}{2}})}^{2}}$

Step 6.6.2

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

$\frac{2 \sqrt{10} \sqrt{p}}{p^{\frac{1}{2} \cdot 2}}$

Step 6.6.3

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

$\frac{2 \sqrt{10} \sqrt{p}}{p^{\frac{2}{2}}}$

Step 6.6.4

Cancel the common factor of $2$ .

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Step 6.6.4.1

Cancel the common factor.

$\frac{2 \sqrt{10} \sqrt{p}}{p^{\frac{2}{2}}}$

Step 6.6.4.2

Rewrite the expression.

$\frac{2 \sqrt{10} \sqrt{p}}{p^{1}}$

Step 6.6.5

Simplify.

$\frac{2 \sqrt{10} \sqrt{p}}{p}$

Step 7

Combine using the product rule for radicals.

$\frac{2 \sqrt{p \cdot 10}}{p}$

Step 8

Move $10$ to the left of $p$ .

$\frac{2 \sqrt{10 p}}{p}$