Basic Math Examples

$\frac{3}{2} \cdot \sqrt{\frac{90}{5}}$

Step 1

Divide $90$ by $5$ .

$\frac{3}{2} \cdot \sqrt{18}$

Step 2

Rewrite $18$ as $3^{2} \cdot 2$ .

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Step 2.1

Factor $9$ out of $18$ .

$\frac{3}{2} \cdot \sqrt{9 (2)}$

Step 2.2

Rewrite $9$ as $3^{2}$ .

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

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

Step 3

Pull terms out from under the radical.

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

Step 4

Multiply $\frac{3}{2} (3 \sqrt{2})$ .

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Step 4.1

Combine $3$ and $\frac{3}{2}$ .

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

Step 4.2

Multiply $3$ by $3$ .

$\frac{9}{2} \sqrt{2}$

Step 4.3

Combine $\frac{9}{2}$ and $\sqrt{2}$ .

$\frac{9 \sqrt{2}}{2}$

$\frac{9 \sqrt{2}}{2}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$\frac{9 \sqrt{2}}{2}$

Decimal Form:

$6.36396103 \dots$

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