Calculus Examples

$\sqrt[3]{32} + \sqrt{8} - \sqrt{18}$

Step 1

Simplify each term.

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Step 1.1

Rewrite $32$ as $2^{3} \cdot 4$ .

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Step 1.1.1

Factor $8$ out of $32$ .

$\sqrt[3]{8 (4)} + \sqrt{8} - \sqrt{18}$

Step 1.1.2

Rewrite $8$ as $2^{3}$ .

$\sqrt[3]{2^{3} \cdot 4} + \sqrt{8} - \sqrt{18}$

$\sqrt[3]{2^{3} \cdot 4} + \sqrt{8} - \sqrt{18}$

Step 1.2

Pull terms out from under the radical.

$2 \sqrt[3]{4} + \sqrt{8} - \sqrt{18}$

Step 1.3

Rewrite $8$ as $2^{2} \cdot 2$ .

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Step 1.3.1

Factor $4$ out of $8$ .

$2 \sqrt[3]{4} + \sqrt{4 (2)} - \sqrt{18}$

Step 1.3.2

Rewrite $4$ as $2^{2}$ .

$2 \sqrt[3]{4} + \sqrt{2^{2} \cdot 2} - \sqrt{18}$

$2 \sqrt[3]{4} + \sqrt{2^{2} \cdot 2} - \sqrt{18}$

Step 1.4

Pull terms out from under the radical.

$2 \sqrt[3]{4} + 2 \sqrt{2} - \sqrt{18}$

Step 1.5

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

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Step 1.5.1

Factor $9$ out of $18$ .

$2 \sqrt[3]{4} + 2 \sqrt{2} - \sqrt{9 (2)}$

Step 1.5.2

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

$2 \sqrt[3]{4} + 2 \sqrt{2} - \sqrt{3^{2} \cdot 2}$

$2 \sqrt[3]{4} + 2 \sqrt{2} - \sqrt{3^{2} \cdot 2}$

Step 1.6

Pull terms out from under the radical.

$2 \sqrt[3]{4} + 2 \sqrt{2} - (3 \sqrt{2})$

Step 1.7

Multiply $3$ by $- 1$ .

$2 \sqrt[3]{4} + 2 \sqrt{2} - 3 \sqrt{2}$

$2 \sqrt[3]{4} + 2 \sqrt{2} - 3 \sqrt{2}$

Step 2

Subtract $3 \sqrt{2}$ from $2 \sqrt{2}$ .

$2 \sqrt[3]{4} - \sqrt{2}$

Step 3

The result can be shown in multiple forms.

Exact Form:

$2 \sqrt[3]{4} - \sqrt{2}$

Decimal Form:

$1.76058854 \dots$

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