Algebra Examples

$\frac{\sqrt{2} \sqrt{10}}{\sqrt{5}}$

Step 1

Combine $\sqrt{10}$ and $\sqrt{5}$ into a single radical.

$\sqrt{2} \sqrt{\frac{10}{5}}$

Step 2

Combine using the product rule for radicals.

$\sqrt{2 (\frac{10}{5})}$

Step 3

Combine $2$ and $\frac{10}{5}$ .

$\sqrt{\frac{2 \cdot 10}{5}}$

Step 4

Reduce the expression by cancelling the common factors.

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Step 4.1

Reduce the expression $\frac{2 \cdot 10}{5}$ by cancelling the common factors.

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Step 4.1.1

Factor $5$ out of $2 \cdot 10$ .

$\sqrt{\frac{5 (2 \cdot 2)}{5}}$

Step 4.1.2

Factor $5$ out of $5$ .

$\sqrt{\frac{5 (2 \cdot 2)}{5 (1)}}$

Step 4.1.3

Cancel the common factor.

$\sqrt{\frac{5 (2 \cdot 2)}{5 \cdot 1}}$

Step 4.1.4

Rewrite the expression.

$\sqrt{\frac{2 \cdot 2}{1}}$

Step 4.2

Divide $2 \cdot 2$ by $1$ .

$\sqrt{2 \cdot 2}$

Step 5

Multiply $2$ by $2$ .

$\sqrt{4}$

Step 6

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

$\sqrt{2^{2}}$

Step 7

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

$2$