Algebra Examples

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

Rewrite $- 5$ as $- 1 (5)$ .

$\sqrt{- 1 (5)} \cdot \sqrt{20}$

Rewrite $\sqrt{- 1 (5)}$ as $\sqrt{- 1} \cdot \sqrt{5}$ .

$\sqrt{- 1} \cdot \sqrt{5} \cdot \sqrt{20}$

Rewrite $\sqrt{- 1}$ as $i$ .

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

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

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Factor $4$ out of $20$ .

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

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

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

Pull terms out from under the radical.

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

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

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

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

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

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

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

$i (2 {\sqrt{5}}^{1 + 1})$

Add $1$ and $1$ .

$i (2 {\sqrt{5}}^{2})$

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

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

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

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

$i (2 \cdot 5^{\frac{1}{2} \cdot 2})$

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

$i (2 \cdot 5^{\frac{2}{2}})$

Cancel the common factor of $2$ .

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Cancel the common factor.

$i (2 \cdot 5^{\frac{2}{2}})$

Rewrite the expression.

$i (2 \cdot 5^{1})$

Evaluate the exponent.

$i (2 \cdot 5)$

Simplify the expression.

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Multiply $2$ by $5$ .

$i \cdot 10$

Move $10$ to the left of $i$ .

$10 i$