Algebra Examples

$2 \sqrt{24} \cdot \frac{5}{\sqrt{4}}$

Step 1

Simplify the denominator.

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Step 1.1

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

$2 \sqrt{24} \cdot \frac{5}{\sqrt{2^{2}}}$

Step 1.2

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

$2 \sqrt{24} \cdot \frac{5}{2}$

$2 \sqrt{24} \cdot \frac{5}{2}$

Step 2

Cancel the common factor of $2$ .

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Step 2.1

Factor $2$ out of $2 \sqrt{24}$ .

$2 (\sqrt{24}) \cdot \frac{5}{2}$

Step 2.2

Cancel the common factor.

$2 \sqrt{24} \cdot \frac{5}{2}$

Step 2.3

Rewrite the expression.

$\sqrt{24} \cdot 5$

$\sqrt{24} \cdot 5$

Step 3

Rewrite $24$ as $2^{2} \cdot 6$ .

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Step 3.1

Factor $4$ out of $24$ .

$\sqrt{4 (6)} \cdot 5$

Step 3.2

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

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

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

Step 4

Pull terms out from under the radical.

$2 \sqrt{6} \cdot 5$

Step 5

Multiply $5$ by $2$ .

$10 \sqrt{6}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$10 \sqrt{6}$

Decimal Form:

$24.49489742 \dots$

$[\begin{array}{c} x^{2} & \frac{1}{2} \\ \sqrt{π} & \int x d x \end{array}]$