Algebra Examples

$\sqrt{\frac{14}{3}} \cdot \sqrt{\frac{21}{2}}$

Step 1

Combine using the product rule for radicals.

$\sqrt{\frac{14}{3} \cdot \frac{21}{2}}$

Step 2

Multiply $\frac{14}{3}$ by $\frac{21}{2}$ .

$\sqrt{\frac{14 \cdot 21}{3 \cdot 2}}$

Step 3

Reduce the expression $\frac{14 \cdot 21}{3 \cdot 2}$ by cancelling the common factors.

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Step 3.1

Factor $2$ out of $14 \cdot 21$ .

$\sqrt{\frac{2 (7 \cdot 21)}{3 \cdot 2}}$

Step 3.2

Factor $2$ out of $3 \cdot 2$ .

$\sqrt{\frac{2 (7 \cdot 21)}{2 \cdot 3}}$

Step 3.3

Cancel the common factor.

$\sqrt{\frac{2 (7 \cdot 21)}{2 \cdot 3}}$

Step 3.4

Rewrite the expression.

$\sqrt{\frac{7 \cdot 21}{3}}$

Step 4

Cancel the common factor of $21$ and $3$ .

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Step 4.1

Factor $3$ out of $7 \cdot 21$ .

$\sqrt{\frac{3 (7 \cdot 7)}{3}}$

Step 4.2

Cancel the common factors.

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Step 4.2.1

Factor $3$ out of $3$ .

$\sqrt{\frac{3 (7 \cdot 7)}{3 (1)}}$

Step 4.2.2

Cancel the common factor.

$\sqrt{\frac{3 (7 \cdot 7)}{3 \cdot 1}}$

Step 4.2.3

Rewrite the expression.

$\sqrt{\frac{7 \cdot 7}{1}}$

Step 4.2.4

Divide $7 \cdot 7$ by $1$ .

$\sqrt{7 \cdot 7}$

Step 5

Write the expression using exponents.

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Step 5.1

Multiply $7$ by $7$ .

$\sqrt{49}$

Step 5.2

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

$\sqrt{7^{2}}$

Step 6

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

$7$