Basic Math Examples

$\frac{\sqrt{49}}{\sqrt{81}} \cdot (\sqrt{0.09})$

Step 1

Simplify the numerator.

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Step 1.1

Rewrite $49$ as $7^{2}$ .

$\frac{\sqrt{7^{2}}}{\sqrt{81}} \cdot \sqrt{0.09}$

Step 1.2

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

$\frac{7}{\sqrt{81}} \cdot \sqrt{0.09}$

Step 2

Simplify the denominator.

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Step 2.1

Rewrite $81$ as $9^{2}$ .

$\frac{7}{\sqrt{9^{2}}} \cdot \sqrt{0.09}$

Step 2.2

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

$\frac{7}{9} \cdot \sqrt{0.09}$

Step 3

Rewrite $0.09$ as ${0.3}^{2}$ .

$\frac{7}{9} \cdot \sqrt{{0.3}^{2}}$

Step 4

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

$\frac{7}{9} \cdot 0.3$

Step 5

Cancel the common factor of $0.3$ .

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Step 5.1

Factor $0.3$ out of $9$ .

$\frac{7}{0.3 (30)} \cdot 0.3$

Step 5.2

Cancel the common factor.

$\frac{7}{0.3 \cdot 30} \cdot 0.3$

Step 5.3

Rewrite the expression.

$\frac{7}{30}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$\frac{7}{30}$

Decimal Form:

$0.2\overline{3}$