Basic Math Examples

$i \sqrt{- 98} \cdot \sqrt{98}$

Step 1

Rewrite $- 98$ as $- 1 (98)$ .

$i \sqrt{- 1 (98)} \cdot \sqrt{98}$

Step 2

Rewrite $\sqrt{- 1 (98)}$ as $\sqrt{- 1} \cdot \sqrt{98}$ .

$i (\sqrt{- 1} \cdot \sqrt{98}) \cdot \sqrt{98}$

Step 3

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

$i (i \cdot \sqrt{98}) \cdot \sqrt{98}$

Step 4

Rewrite $98$ as $7^{2} \cdot 2$ .

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Step 4.1

Factor $49$ out of $98$ .

$i (i \cdot \sqrt{49 (2)}) \cdot \sqrt{98}$

Step 4.2

Rewrite $49$ as $7^{2}$ .

$i (i \cdot \sqrt{7^{2} \cdot 2}) \cdot \sqrt{98}$

Step 5

Pull terms out from under the radical.

$i (i \cdot (7 \sqrt{2})) \cdot \sqrt{98}$

Step 6

Move $7$ to the left of $i$ .

$i (7 \cdot i \sqrt{2}) \cdot \sqrt{98}$

Step 7

Multiply $i (7 i \sqrt{2})$ .

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Step 7.1

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

$7 (i^{1} i) \sqrt{2} \cdot \sqrt{98}$

Step 7.2

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

$7 (i^{1} i^{1}) \sqrt{2} \cdot \sqrt{98}$

Step 7.3

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

$7 i^{1 + 1} \sqrt{2} \cdot \sqrt{98}$

Step 7.4

Add $1$ and $1$ .

$7 i^{2} \sqrt{2} \cdot \sqrt{98}$

Step 8

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

$7 \cdot - 1 \sqrt{2} \cdot \sqrt{98}$

Step 9

Multiply $7$ by $- 1$ .

$- 7 \sqrt{2} \cdot \sqrt{98}$

Step 10

Rewrite $98$ as $7^{2} \cdot 2$ .

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Step 10.1

Factor $49$ out of $98$ .

$- 7 \sqrt{2} \cdot \sqrt{49 (2)}$

Step 10.2

Rewrite $49$ as $7^{2}$ .

$- 7 \sqrt{2} \cdot \sqrt{7^{2} \cdot 2}$

Step 11

Pull terms out from under the radical.

$- 7 \sqrt{2} \cdot (7 \sqrt{2})$

Step 12

Multiply $- 7 \sqrt{2} (7 \sqrt{2})$ .

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Step 12.1

Multiply $7$ by $- 7$ .

$- 49 \sqrt{2} \sqrt{2}$

Step 12.2

Raise $\sqrt{2}$ to the power of $1$ .

$- 49 ({\sqrt{2}}^{1} \sqrt{2})$

Step 12.3

Raise $\sqrt{2}$ to the power of $1$ .

$- 49 ({\sqrt{2}}^{1} {\sqrt{2}}^{1})$

Step 12.4

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

$- 49 {\sqrt{2}}^{1 + 1}$

Step 12.5

Add $1$ and $1$ .

$- 49 {\sqrt{2}}^{2}$

Step 13

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

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Step 13.1

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

$- 49 {(2^{\frac{1}{2}})}^{2}$

Step 13.2

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

$- 49 \cdot 2^{\frac{1}{2} \cdot 2}$

Step 13.3

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

$- 49 \cdot 2^{\frac{2}{2}}$

Step 13.4

Cancel the common factor of $2$ .

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Step 13.4.1

Cancel the common factor.

$- 49 \cdot 2^{\frac{2}{2}}$

Step 13.4.2

Rewrite the expression.

$- 49 \cdot 2^{1}$

Step 13.5

Evaluate the exponent.

$- 49 \cdot 2$

Step 14

Multiply $- 49$ by $2$ .

$- 98$