Basic Math Examples

$\frac{1}{2} \cdot ((\sqrt{21}) (\sqrt{50}))$

Step 1

Combine using the product rule for radicals.

$\frac{1}{2} \cdot \sqrt{21 \cdot 50}$

Step 2

Multiply $21$ by $50$ .

$\frac{1}{2} \cdot \sqrt{1050}$

Step 3

Rewrite $1050$ as $5^{2} \cdot 42$ .

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Step 3.1

Factor $25$ out of $1050$ .

$\frac{1}{2} \cdot \sqrt{25 (42)}$

Step 3.2

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

$\frac{1}{2} \cdot \sqrt{5^{2} \cdot 42}$

$\frac{1}{2} \cdot \sqrt{5^{2} \cdot 42}$

Step 4

Pull terms out from under the radical.

$\frac{1}{2} \cdot (5 \sqrt{42})$

Step 5

Multiply $\frac{1}{2} (5 \sqrt{42})$ .

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Step 5.1

Combine $5$ and $\frac{1}{2}$ .

$\frac{5}{2} \sqrt{42}$

Step 5.2

Combine $\frac{5}{2}$ and $\sqrt{42}$ .

$\frac{5 \sqrt{42}}{2}$

$\frac{5 \sqrt{42}}{2}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$\frac{5 \sqrt{42}}{2}$

Decimal Form:

$16.20185174 \dots$

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