Algebra Examples

$\sqrt{\frac{18}{81}}$

Step 1

Cancel the common factor of $18$ and $81$ .

Tap for more steps...

Step 1.1

Factor $9$ out of $18$ .

$\sqrt{\frac{9 (2)}{81}}$

Step 1.2

Cancel the common factors.

Tap for more steps...

Step 1.2.1

Factor $9$ out of $81$ .

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

Step 1.2.2

Cancel the common factor.

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

Step 1.2.3

Rewrite the expression.

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

Step 2

Rewrite $\sqrt{\frac{2}{9}}$ as $\frac{\sqrt{2}}{\sqrt{9}}$ .

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

Step 3

Simplify the denominator.

Tap for more steps...

Step 3.1

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

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

Step 3.2

Pull terms out from under the radical.

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

Step 3.3

The absolute value is the distance between a number and zero. The distance between $0$ and $3$ is $3$ .

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

Step 4

The result can be shown in multiple forms.

Exact Form:

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

Decimal Form:

$0.47140452 \dots$