Multiply ( square root of 49)/( square root of 81)*( square root of 0.09)

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

Simplify the numerator.

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

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

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

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

Simplify the denominator.

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

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

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

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

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

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

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

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

Cancel the common factor of $0.3$ .

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Factor $0.3$ out of $9$ .

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

Cancel the common factor.

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

Rewrite the expression.

$\frac{7}{30}$

The result can be shown in multiple forms.

Exact Form:

$\frac{7}{30}$

Decimal Form:

$0.2\overline{3}$

Multiply ( square root of 49)/( square root of 81)*( square root of 0.09)