Basic Math Examples

$\frac{21 - i \sqrt{18}}{3}$

Step 1

Simplify the numerator.

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Step 1.1

Rewrite $18$ as $3^{2} \cdot 2$ .

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Step 1.1.1

Factor $9$ out of $18$ .

$\frac{21 - i \sqrt{9 (2)}}{3}$

Step 1.1.2

Rewrite $9$ as $3^{2}$ .

$\frac{21 - i \sqrt{3^{2} \cdot 2}}{3}$

$\frac{21 - i \sqrt{3^{2} \cdot 2}}{3}$

Step 1.2

Pull terms out from under the radical.

$\frac{21 - i (3 \sqrt{2})}{3}$

Step 1.3

Multiply $3$ by $- 1$ .

$\frac{21 - 3 i \sqrt{2}}{3}$

$\frac{21 - 3 i \sqrt{2}}{3}$

Step 2

Cancel the common factor of $21 - 3 i \sqrt{2}$ and $3$ .

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Step 2.1

Factor $3$ out of $21$ .

$\frac{3 \cdot 7 - 3 i \sqrt{2}}{3}$

Step 2.2

Factor $3$ out of $- 3 i \sqrt{2}$ .

$\frac{3 \cdot 7 + 3 (- i \sqrt{2})}{3}$

Step 2.3

Factor $3$ out of $3 (7) + 3 (- i \sqrt{2})$ .

$\frac{3 (7 - i \sqrt{2})}{3}$

Step 2.4

Cancel the common factors.

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Step 2.4.1

Factor $3$ out of $3$ .

$\frac{3 (7 - i \sqrt{2})}{3 (1)}$

Step 2.4.2

Cancel the common factor.

$\frac{3 (7 - i \sqrt{2})}{3 \cdot 1}$

Step 2.4.3

Rewrite the expression.

$\frac{7 - i \sqrt{2}}{1}$

Step 2.4.4

Divide $7 - i \sqrt{2}$ by $1$ .

$7 - i \sqrt{2}$

$7 - i \sqrt{2}$

$7 - i \sqrt{2}$

$[\begin{array}{c} x^{2} & \frac{1}{2} \\ \sqrt{π} & \int x d x \end{array}]$