Basic Math Examples

$i^{47} - \sqrt{- 25}$

Step 1

Simplify each term.

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Step 1.1

Rewrite $i^{47}$ as ${(i^{4})}^{11} (i^{2} \cdot i)$ .

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Step 1.1.1

Factor out $i^{44}$ .

$i^{44} i^{3} - \sqrt{- 25}$

Step 1.1.2

Rewrite $i^{44}$ as ${(i^{4})}^{11}$ .

${(i^{4})}^{11} i^{3} - \sqrt{- 25}$

Step 1.1.3

Factor out $i^{2}$ .

${(i^{4})}^{11} (i^{2} \cdot i) - \sqrt{- 25}$

Step 1.2

Rewrite $i^{4}$ as $1$ .

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Step 1.2.1

Rewrite $i^{4}$ as ${(i^{2})}^{2}$ .

${({(i^{2})}^{2})}^{11} (i^{2} \cdot i) - \sqrt{- 25}$

Step 1.2.2

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

${({(- 1)}^{2})}^{11} (i^{2} \cdot i) - \sqrt{- 25}$

Step 1.2.3

Raise $- 1$ to the power of $2$ .

$1^{11} (i^{2} \cdot i) - \sqrt{- 25}$

Step 1.3

One to any power is one.

$1 (i^{2} \cdot i) - \sqrt{- 25}$

Step 1.4

Multiply $i^{2} \cdot i$ by $1$ .

$i^{2} \cdot i - \sqrt{- 25}$

Step 1.5

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

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

Step 1.6

Rewrite $- 1 i$ as $- i$ .

$- i - \sqrt{- 25}$

Step 1.7

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

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

Step 1.8

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

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

Step 1.9

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

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

Step 1.10

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

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

Step 1.11

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

$- i - (i \cdot 5)$

Step 1.12

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

$- i - (5 \cdot i)$

Step 1.13

Multiply $5$ by $- 1$ .

$- i - 5 i$

Step 2

Subtract $5 i$ from $- i$ .

$- 6 i$