Algebra Examples

$\frac{1}{3} \sqrt{- 25}$

Step 1

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

$\frac{1}{3} \cdot \sqrt{- 1 (25)}$

Step 2

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

$\frac{1}{3} \cdot (\sqrt{- 1} \cdot \sqrt{25})$

Step 3

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

$\frac{1}{3} \cdot (i \cdot \sqrt{25})$

Step 4

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

$\frac{1}{3} \cdot (i \cdot \sqrt{5^{2}})$

Step 5

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

$\frac{1}{3} \cdot (i \cdot 5)$

Step 6

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

$\frac{1}{3} \cdot (5 \cdot i)$

Step 7

Multiply $\frac{1}{3} (5 i)$ .

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Step 7.1

Combine $5$ and $\frac{1}{3}$ .

$\frac{5}{3} i$

Step 7.2

Combine $\frac{5}{3}$ and $i$ .

$\frac{5 i}{3}$