Algebra Examples

$\sqrt{- 4} \cdot \sqrt{- 25}$

Rewrite $- 4$ as $- 1 (4)$ .

$\sqrt{- 1 (4)} \cdot \sqrt{- 25}$

Rewrite $\sqrt{- 1 (4)}$ as $\sqrt{- 1} \cdot \sqrt{4}$ .

$\sqrt{- 1} \cdot \sqrt{4} \cdot \sqrt{- 25}$

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

$i \cdot \sqrt{4} \cdot \sqrt{- 25}$

Rewrite $- 25$ as $- 1 (25)$ .

$i \cdot \sqrt{4} \cdot \sqrt{- 1 (25)}$

Rewrite $\sqrt{- 1 (25)}$ as $\sqrt{- 1} \cdot \sqrt{25}$ .

$i \cdot \sqrt{4} \cdot (\sqrt{- 1} \cdot \sqrt{25})$

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

$i \cdot \sqrt{4} \cdot (i \cdot \sqrt{25})$

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

$i \cdot \sqrt{2^{2}} \cdot (i \cdot \sqrt{25})$

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

$i \cdot 2 \cdot (i \cdot \sqrt{25})$

Move $2$ to the left of $i$ .

$2 \cdot i \cdot (i \cdot \sqrt{25})$

Rewrite $25$ as $5^{2}$ .

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

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

$2 i \cdot (i \cdot 5)$

Move $5$ to the left of $i$ .

$2 i \cdot (5 \cdot i)$

Multiply $2 i (5 i)$ .

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Multiply $5$ by $2$ .

$10 i i$

Raise $i$ to the power of $1$ .

$10 (i^{1} i)$

Raise $i$ to the power of $1$ .

$10 (i^{1} i^{1})$

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

$10 i^{1 + 1}$

Add $1$ and $1$ .

$10 i^{2}$

Rewrite $i^{2}$ as $- 1$ .

$10 \cdot - 1$

Multiply $10$ by $- 1$ .

$- 10$