Algebra Examples

$\frac{50 \sqrt{3}}{\sqrt{2}} \cdot \frac{80 \sqrt{5}}{\sqrt{3}}$

Step 1

Cancel the common factor of $\sqrt{3}$ .

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Step 1.1

Factor $\sqrt{3}$ out of $50 \sqrt{3}$ .

$\frac{\sqrt{3} \cdot 50}{\sqrt{2}} \cdot \frac{80 \sqrt{5}}{\sqrt{3}}$

Step 1.2

Cancel the common factor.

$\frac{\sqrt{3} \cdot 50}{\sqrt{2}} \cdot \frac{80 \sqrt{5}}{\sqrt{3}}$

Step 1.3

Rewrite the expression.

$\frac{50}{\sqrt{2}} \cdot (80 \sqrt{5})$

Step 2

Combine $80$ and $\frac{50}{\sqrt{2}}$ .

$\frac{80 \cdot 50}{\sqrt{2}} \cdot \sqrt{5}$

Step 3

Multiply $80$ by $50$ .

$\frac{4000}{\sqrt{2}} \cdot \sqrt{5}$

Step 4

Combine $\frac{4000}{\sqrt{2}}$ and $\sqrt{5}$ .

$\frac{4000 \sqrt{5}}{\sqrt{2}}$

Step 5

Multiply $\frac{4000 \sqrt{5}}{\sqrt{2}}$ by $\frac{\sqrt{2}}{\sqrt{2}}$ .

$\frac{4000 \sqrt{5}}{\sqrt{2}} \cdot \frac{\sqrt{2}}{\sqrt{2}}$

Step 6

Combine and simplify the denominator.

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Step 6.1

Multiply $\frac{4000 \sqrt{5}}{\sqrt{2}}$ by $\frac{\sqrt{2}}{\sqrt{2}}$ .

$\frac{4000 \sqrt{5} \sqrt{2}}{\sqrt{2} \sqrt{2}}$

Step 6.2

Raise $\sqrt{2}$ to the power of $1$ .

$\frac{4000 \sqrt{5} \sqrt{2}}{{\sqrt{2}}^{1} \sqrt{2}}$

Step 6.3

Raise $\sqrt{2}$ to the power of $1$ .

$\frac{4000 \sqrt{5} \sqrt{2}}{{\sqrt{2}}^{1} {\sqrt{2}}^{1}}$

Step 6.4

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

$\frac{4000 \sqrt{5} \sqrt{2}}{{\sqrt{2}}^{1 + 1}}$

Step 6.5

Add $1$ and $1$ .

$\frac{4000 \sqrt{5} \sqrt{2}}{{\sqrt{2}}^{2}}$

Step 6.6

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

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Step 6.6.1

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

$\frac{4000 \sqrt{5} \sqrt{2}}{{(2^{\frac{1}{2}})}^{2}}$

Step 6.6.2

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

$\frac{4000 \sqrt{5} \sqrt{2}}{2^{\frac{1}{2} \cdot 2}}$

Step 6.6.3

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

$\frac{4000 \sqrt{5} \sqrt{2}}{2^{\frac{2}{2}}}$

Step 6.6.4

Cancel the common factor of $2$ .

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Step 6.6.4.1

Cancel the common factor.

$\frac{4000 \sqrt{5} \sqrt{2}}{2^{\frac{2}{2}}}$

Step 6.6.4.2

Rewrite the expression.

$\frac{4000 \sqrt{5} \sqrt{2}}{2^{1}}$

Step 6.6.5

Evaluate the exponent.

$\frac{4000 \sqrt{5} \sqrt{2}}{2}$

Step 7

Cancel the common factor of $4000$ and $2$ .

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Step 7.1

Factor $2$ out of $4000 \sqrt{5} \sqrt{2}$ .

$\frac{2 (2000 \sqrt{5} \sqrt{2})}{2}$

Step 7.2

Cancel the common factors.

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Step 7.2.1

Factor $2$ out of $2$ .

$\frac{2 (2000 \sqrt{5} \sqrt{2})}{2 (1)}$

Step 7.2.2

Cancel the common factor.

$\frac{2 (2000 \sqrt{5} \sqrt{2})}{2 \cdot 1}$

Step 7.2.3

Rewrite the expression.

$\frac{2000 \sqrt{5} \sqrt{2}}{1}$

Step 7.2.4

Divide $2000 \sqrt{5} \sqrt{2}$ by $1$ .

$2000 \sqrt{5} \sqrt{2}$

Step 8

Multiply $2000 \sqrt{5} \sqrt{2}$ .

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Step 8.1

Combine using the product rule for radicals.

$2000 \sqrt{2 \cdot 5}$

Step 8.2

Multiply $2$ by $5$ .

$2000 \sqrt{10}$

Step 9

The result can be shown in multiple forms.

Exact Form:

$2000 \sqrt{10}$

Decimal Form:

$6324.55532033 \dots$