Algebra Examples

$\sqrt{\frac{7}{9}} \cdot \sqrt{\frac{4}{7}}$

Step 1

Combine using the product rule for radicals.

$\sqrt{\frac{7}{9} \cdot \frac{4}{7}}$

Step 2

Multiply $\frac{7}{9}$ by $\frac{4}{7}$ .

$\sqrt{\frac{7 \cdot 4}{9 \cdot 7}}$

Step 3

Reduce the expression $\frac{7 \cdot 4}{9 \cdot 7}$ by cancelling the common factors.

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Step 3.1

Cancel the common factor.

$\sqrt{\frac{7 \cdot 4}{9 \cdot 7}}$

Step 3.2

Rewrite the expression.

$\sqrt{\frac{4}{9}}$

Step 4

Rewrite $\sqrt{\frac{4}{9}}$ as $\frac{\sqrt{4}}{\sqrt{9}}$ .

$\frac{\sqrt{4}}{\sqrt{9}}$

Step 5

Simplify the numerator.

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Step 5.1

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

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

Step 5.2

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

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

Step 6

Simplify the denominator.

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Step 6.1

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

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

Step 6.2

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

$\frac{2}{3}$

Step 7

The result can be shown in multiple forms.

Exact Form:

$\frac{2}{3}$

Decimal Form:

$0.\overline{6}$