Algebra Examples

$\frac{6 \sqrt{5}}{5 \sqrt{3}}$

Step 1

Multiply $\frac{6 \sqrt{5}}{5 \sqrt{3}}$ by $\frac{\sqrt{3}}{\sqrt{3}}$ .

$\frac{6 \sqrt{5}}{5 \sqrt{3}} \cdot \frac{\sqrt{3}}{\sqrt{3}}$

Step 2

Combine and simplify the denominator.

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Step 2.1

Multiply $\frac{6 \sqrt{5}}{5 \sqrt{3}}$ by $\frac{\sqrt{3}}{\sqrt{3}}$ .

$\frac{6 \sqrt{5} \sqrt{3}}{5 \sqrt{3} \sqrt{3}}$

Step 2.2

Move $\sqrt{3}$ .

$\frac{6 \sqrt{5} \sqrt{3}}{5 (\sqrt{3} \sqrt{3})}$

Step 2.3

Raise $\sqrt{3}$ to the power of $1$ .

$\frac{6 \sqrt{5} \sqrt{3}}{5 ({\sqrt{3}}^{1} \sqrt{3})}$

Step 2.4

Raise $\sqrt{3}$ to the power of $1$ .

$\frac{6 \sqrt{5} \sqrt{3}}{5 ({\sqrt{3}}^{1} {\sqrt{3}}^{1})}$

Step 2.5

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

$\frac{6 \sqrt{5} \sqrt{3}}{5 {\sqrt{3}}^{1 + 1}}$

Step 2.6

Add $1$ and $1$ .

$\frac{6 \sqrt{5} \sqrt{3}}{5 {\sqrt{3}}^{2}}$

Step 2.7

Rewrite ${\sqrt{3}}^{2}$ as $3$ .

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Step 2.7.1

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{3}$ as $3^{\frac{1}{2}}$ .

$\frac{6 \sqrt{5} \sqrt{3}}{5 {(3^{\frac{1}{2}})}^{2}}$

Step 2.7.2

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

$\frac{6 \sqrt{5} \sqrt{3}}{5 \cdot 3^{\frac{1}{2} \cdot 2}}$

Step 2.7.3

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

$\frac{6 \sqrt{5} \sqrt{3}}{5 \cdot 3^{\frac{2}{2}}}$

Step 2.7.4

Cancel the common factor of $2$ .

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Step 2.7.4.1

Cancel the common factor.

$\frac{6 \sqrt{5} \sqrt{3}}{5 \cdot 3^{\frac{2}{2}}}$

Step 2.7.4.2

Rewrite the expression.

$\frac{6 \sqrt{5} \sqrt{3}}{5 \cdot 3^{1}}$

Step 2.7.5

Evaluate the exponent.

$\frac{6 \sqrt{5} \sqrt{3}}{5 \cdot 3}$

Step 3

Cancel the common factor of $6$ and $3$ .

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Step 3.1

Factor $3$ out of $6 \sqrt{5} \sqrt{3}$ .

$\frac{3 (2 \sqrt{5} \sqrt{3})}{5 \cdot 3}$

Step 3.2

Cancel the common factors.

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Step 3.2.1

Factor $3$ out of $5 \cdot 3$ .

$\frac{3 (2 \sqrt{5} \sqrt{3})}{3 \cdot 5}$

Step 3.2.2

Cancel the common factor.

$\frac{3 (2 \sqrt{5} \sqrt{3})}{3 \cdot 5}$

Step 3.2.3

Rewrite the expression.

$\frac{2 \sqrt{5} \sqrt{3}}{5}$

Step 4

Simplify the numerator.

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Step 4.1

Combine using the product rule for radicals.

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

Step 4.2

Multiply $3$ by $5$ .

$\frac{2 \sqrt{15}}{5}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$\frac{2 \sqrt{15}}{5}$

Decimal Form:

$1.54919333 \dots$