Algebra Examples

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

Step 1

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

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

Step 2

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

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

Step 3

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

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

Step 4

Remove unnecessary parentheses.

$\sqrt{- 5 i \sqrt{5}}$

Step 5

Rewrite $- 5 i \sqrt{5}$ as $i^{2} \cdot (5 i \sqrt{5})$ .

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Step 5.1

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

$\sqrt{- 1 (5) i \sqrt{5}}$

Step 5.2

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

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

Step 5.3

Add parentheses.

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

Step 5.4

Add parentheses.

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

Step 6

Pull terms out from under the radical.

$i \sqrt{5 i \sqrt{5}}$