Algebra Examples

$\frac{\sqrt{8}}{2 \sqrt{9}}$

Step 1

Simplify the numerator.

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Step 1.1

Rewrite $8$ as $2^{2} \cdot 2$ .

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Step 1.1.1

Factor $4$ out of $8$ .

$\frac{\sqrt{4 (2)}}{2 \sqrt{9}}$

Step 1.1.2

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

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

Step 1.2

Pull terms out from under the radical.

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

Step 2

Simplify the denominator.

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Step 2.1

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

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

Step 2.2

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

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

Step 3

Reduce the expression by cancelling the common factors.

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Step 3.1

Multiply $2$ by $3$ .

$\frac{2 \sqrt{2}}{6}$

Step 3.2

Cancel the common factor of $2$ and $6$ .

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Step 3.2.1

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

$\frac{2 (\sqrt{2})}{6}$

Step 3.2.2

Cancel the common factors.

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Step 3.2.2.1

Factor $2$ out of $6$ .

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

Step 3.2.2.2

Cancel the common factor.

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

Step 3.2.2.3

Rewrite the expression.

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

Step 4

The result can be shown in multiple forms.

Exact Form:

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

Decimal Form:

$0.47140452 \dots$