Algebra Examples

$- \sqrt{5} \cdot \sqrt{20}$

Step 1

Rewrite $20$ as $2^{2} \cdot 5$ .

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Step 1.1

Factor $4$ out of $20$ .

$- \sqrt{5} \cdot \sqrt{4 (5)}$

Step 1.2

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

$- \sqrt{5} \cdot \sqrt{2^{2} \cdot 5}$

Step 2

Pull terms out from under the radical.

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

Step 3

Multiply $- \sqrt{5} (2 \sqrt{5})$ .

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Step 3.1

Multiply $2$ by $- 1$ .

$- 2 \sqrt{5} \sqrt{5}$

Step 3.2

Raise $\sqrt{5}$ to the power of $1$ .

$- 2 ({\sqrt{5}}^{1} \sqrt{5})$

Step 3.3

Raise $\sqrt{5}$ to the power of $1$ .

$- 2 ({\sqrt{5}}^{1} {\sqrt{5}}^{1})$

Step 3.4

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$- 2 {\sqrt{5}}^{1 + 1}$

Step 3.5

Add $1$ and $1$ .

$- 2 {\sqrt{5}}^{2}$

Step 4

Rewrite ${\sqrt{5}}^{2}$ as $5$ .

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Step 4.1

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{5}$ as $5^{\frac{1}{2}}$ .

$- 2 {(5^{\frac{1}{2}})}^{2}$

Step 4.2

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

$- 2 \cdot 5^{\frac{1}{2} \cdot 2}$

Step 4.3

Combine $\frac{1}{2}$ and $2$ .

$- 2 \cdot 5^{\frac{2}{2}}$

Step 4.4

Cancel the common factor of $2$ .

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Step 4.4.1

Cancel the common factor.

$- 2 \cdot 5^{\frac{2}{2}}$

Step 4.4.2

Rewrite the expression.

$- 2 \cdot 5^{1}$

Step 4.5

Evaluate the exponent.

$- 2 \cdot 5$

Step 5

Multiply $- 2$ by $5$ .

$- 10$