Basic Math Examples

$\frac{1}{2} \cdot \sqrt{10} \cdot \sqrt{125}$

Step 1

Combine $\frac{1}{2}$ and $\sqrt{10}$ .

$\frac{\sqrt{10}}{2} \cdot \sqrt{125}$

Step 2

Rewrite $125$ as $5^{2} \cdot 5$ .

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Step 2.1

Factor $25$ out of $125$ .

$\frac{\sqrt{10}}{2} \cdot \sqrt{25 (5)}$

Step 2.2

Rewrite $25$ as $5^{2}$ .

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

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

Step 3

Pull terms out from under the radical.

$\frac{\sqrt{10}}{2} \cdot (5 \sqrt{5})$

Step 4

Multiply $\frac{\sqrt{10}}{2} (5 \sqrt{5})$ .

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Step 4.1

Combine $5$ and $\frac{\sqrt{10}}{2}$ .

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

Step 4.2

Combine $\frac{5 \sqrt{10}}{2}$ and $\sqrt{5}$ .

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

Step 4.3

Combine using the product rule for radicals.

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

Step 4.4

Multiply $5$ by $10$ .

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

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

Step 5

Simplify the numerator.

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Step 5.1

Rewrite $50$ as $5^{2} \cdot 2$ .

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Step 5.1.1

Factor $25$ out of $50$ .

$\frac{5 \sqrt{25 (2)}}{2}$

Step 5.1.2

Rewrite $25$ as $5^{2}$ .

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

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

Step 5.2

Pull terms out from under the radical.

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

Step 5.3

Multiply $5$ by $5$ .

$\frac{25 \sqrt{2}}{2}$

$\frac{25 \sqrt{2}}{2}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$\frac{25 \sqrt{2}}{2}$

Decimal Form:

$17.67766952 \dots$

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