Algebra Examples

$\frac{5 \sqrt{4}}{3 \sqrt{5}}$

Step 1

Simplify the numerator.

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Step 1.1

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

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

Step 1.2

Pull terms out from under the radical, assuming positive real numbers.

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

Step 2

Multiply $5$ by $2$ .

$\frac{10}{3 \sqrt{5}}$

Step 3

Multiply $\frac{10}{3 \sqrt{5}}$ by $\frac{\sqrt{5}}{\sqrt{5}}$ .

$\frac{10}{3 \sqrt{5}} \cdot \frac{\sqrt{5}}{\sqrt{5}}$

Step 4

Combine and simplify the denominator.

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Step 4.1

Multiply $\frac{10}{3 \sqrt{5}}$ by $\frac{\sqrt{5}}{\sqrt{5}}$ .

$\frac{10 \sqrt{5}}{3 \sqrt{5} \sqrt{5}}$

Step 4.2

Move $\sqrt{5}$ .

$\frac{10 \sqrt{5}}{3 (\sqrt{5} \sqrt{5})}$

Step 4.3

Raise $\sqrt{5}$ to the power of $1$ .

$\frac{10 \sqrt{5}}{3 ({\sqrt{5}}^{1} \sqrt{5})}$

Step 4.4

Raise $\sqrt{5}$ to the power of $1$ .

$\frac{10 \sqrt{5}}{3 ({\sqrt{5}}^{1} {\sqrt{5}}^{1})}$

Step 4.5

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

$\frac{10 \sqrt{5}}{3 {\sqrt{5}}^{1 + 1}}$

Step 4.6

Add $1$ and $1$ .

$\frac{10 \sqrt{5}}{3 {\sqrt{5}}^{2}}$

Step 4.7

Rewrite ${\sqrt{5}}^{2}$ as $5$ .

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Step 4.7.1

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{5}$ as $5^{\frac{1}{2}}$ .

$\frac{10 \sqrt{5}}{3 {(5^{\frac{1}{2}})}^{2}}$

Step 4.7.2

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

$\frac{10 \sqrt{5}}{3 \cdot 5^{\frac{1}{2} \cdot 2}}$

Step 4.7.3

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

$\frac{10 \sqrt{5}}{3 \cdot 5^{\frac{2}{2}}}$

Step 4.7.4

Cancel the common factor of $2$ .

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Step 4.7.4.1

Cancel the common factor.

$\frac{10 \sqrt{5}}{3 \cdot 5^{\frac{2}{2}}}$

Step 4.7.4.2

Rewrite the expression.

$\frac{10 \sqrt{5}}{3 \cdot 5^{1}}$

Step 4.7.5

Evaluate the exponent.

$\frac{10 \sqrt{5}}{3 \cdot 5}$

Step 5

Cancel the common factor of $10$ and $5$ .

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Step 5.1

Factor $5$ out of $10 \sqrt{5}$ .

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

Step 5.2

Cancel the common factors.

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Step 5.2.1

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

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

Step 5.2.2

Cancel the common factor.

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

Step 5.2.3

Rewrite the expression.

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

Step 6

The result can be shown in multiple forms.

Exact Form:

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

Decimal Form:

$1.49071198 \dots$