Pre-Algebra Examples

$\frac{1}{2} \cdot \sqrt{40}$

Step 1

Rewrite $40$ as $2^{2} \cdot 10$ .

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Step 1.1

Factor $4$ out of $40$ .

$\frac{1}{2} \cdot \sqrt{4 (10)}$

Step 1.2

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

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

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

Step 2

Pull terms out from under the radical.

$\frac{1}{2} \cdot (2 \sqrt{10})$

Step 3

Cancel the common factor of $2$ .

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Step 3.1

Factor $2$ out of $2 \sqrt{10}$ .

$\frac{1}{2} \cdot (2 (\sqrt{10}))$

Step 3.2

Cancel the common factor.

$\frac{1}{2} \cdot (2 \sqrt{10})$

Step 3.3

Rewrite the expression.

$\sqrt{10}$

$\sqrt{10}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$\sqrt{10}$

Decimal Form:

$3.16227766 \dots$

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