Finite Math Examples

$2 i \sqrt{3} (i \sqrt{3} - \sqrt{2})$

Step 1

Apply the distributive property.

$2 i \sqrt{3} (i \sqrt{3}) + 2 i \sqrt{3} (- \sqrt{2})$

Step 2

Multiply $2 i \sqrt{3} (i \sqrt{3})$ .

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Step 2.1

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

$2 (i^{1} i) \sqrt{3} \sqrt{3} + 2 i \sqrt{3} (- \sqrt{2})$

Step 2.2

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

$2 (i^{1} i^{1}) \sqrt{3} \sqrt{3} + 2 i \sqrt{3} (- \sqrt{2})$

Step 2.3

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

$2 i^{1 + 1} \sqrt{3} \sqrt{3} + 2 i \sqrt{3} (- \sqrt{2})$

Step 2.4

Add $1$ and $1$ .

$2 i^{2} \sqrt{3} \sqrt{3} + 2 i \sqrt{3} (- \sqrt{2})$

Step 2.5

Raise $\sqrt{3}$ to the power of $1$ .

$2 i^{2} ({\sqrt{3}}^{1} \sqrt{3}) + 2 i \sqrt{3} (- \sqrt{2})$

Step 2.6

Raise $\sqrt{3}$ to the power of $1$ .

$2 i^{2} ({\sqrt{3}}^{1} {\sqrt{3}}^{1}) + 2 i \sqrt{3} (- \sqrt{2})$

Step 2.7

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

$2 i^{2} {\sqrt{3}}^{1 + 1} + 2 i \sqrt{3} (- \sqrt{2})$

Step 2.8

Add $1$ and $1$ .

$2 i^{2} {\sqrt{3}}^{2} + 2 i \sqrt{3} (- \sqrt{2})$

Step 3

Multiply $2 i \sqrt{3} (- \sqrt{2})$ .

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Step 3.1

Multiply $- 1$ by $2$ .

$2 i^{2} {\sqrt{3}}^{2} - 2 i \sqrt{3} \sqrt{2}$

Step 3.2

Combine using the product rule for radicals.

$2 i^{2} {\sqrt{3}}^{2} - 2 i \sqrt{2 \cdot 3}$

Step 3.3

Multiply $2$ by $3$ .

$2 i^{2} {\sqrt{3}}^{2} - 2 i \sqrt{6}$

Step 4

Simplify each term.

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Step 4.1

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

$2 \cdot - 1 {\sqrt{3}}^{2} - 2 i \sqrt{6}$

Step 4.2

Multiply $2$ by $- 1$ .

$- 2 {\sqrt{3}}^{2} - 2 i \sqrt{6}$

Step 4.3

Rewrite ${\sqrt{3}}^{2}$ as $3$ .

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Step 4.3.1

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{3}$ as $3^{\frac{1}{2}}$ .

$- 2 {(3^{\frac{1}{2}})}^{2} - 2 i \sqrt{6}$

Step 4.3.2

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

$- 2 \cdot 3^{\frac{1}{2} \cdot 2} - 2 i \sqrt{6}$

Step 4.3.3

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

$- 2 \cdot 3^{\frac{2}{2}} - 2 i \sqrt{6}$

Step 4.3.4

Cancel the common factor of $2$ .

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Step 4.3.4.1

Cancel the common factor.

$- 2 \cdot 3^{\frac{2}{2}} - 2 i \sqrt{6}$

Step 4.3.4.2

Rewrite the expression.

$- 2 \cdot 3^{1} - 2 i \sqrt{6}$

Step 4.3.5

Evaluate the exponent.

$- 2 \cdot 3 - 2 i \sqrt{6}$

Step 4.4

Multiply $- 2$ by $3$ .

$- 6 - 2 i \sqrt{6}$