Pre-Algebra Examples

$3 \sqrt[4]{32} - \sqrt[4]{162}$

Step 1

Simplify each term.

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Step 1.1

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

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Step 1.1.1

Factor $16$ out of $32$ .

$3 \sqrt[4]{16 (2)} - \sqrt[4]{162}$

Step 1.1.2

Rewrite $16$ as $2^{4}$ .

$3 \sqrt[4]{2^{4} \cdot 2} - \sqrt[4]{162}$

$3 \sqrt[4]{2^{4} \cdot 2} - \sqrt[4]{162}$

Step 1.2

Pull terms out from under the radical.

$3 (2 \sqrt[4]{2}) - \sqrt[4]{162}$

Step 1.3

Multiply $2$ by $3$ .

$6 \sqrt[4]{2} - \sqrt[4]{162}$

Step 1.4

Rewrite $162$ as $3^{4} \cdot 2$ .

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Step 1.4.1

Factor $81$ out of $162$ .

$6 \sqrt[4]{2} - \sqrt[4]{81 (2)}$

Step 1.4.2

Rewrite $81$ as $3^{4}$ .

$6 \sqrt[4]{2} - \sqrt[4]{3^{4} \cdot 2}$

$6 \sqrt[4]{2} - \sqrt[4]{3^{4} \cdot 2}$

Step 1.5

Pull terms out from under the radical.

$6 \sqrt[4]{2} - (3 \sqrt[4]{2})$

Step 1.6

Multiply $3$ by $- 1$ .

$6 \sqrt[4]{2} - 3 \sqrt[4]{2}$

$6 \sqrt[4]{2} - 3 \sqrt[4]{2}$

Step 2

Subtract $3 \sqrt[4]{2}$ from $6 \sqrt[4]{2}$ .

$3 \sqrt[4]{2}$

Step 3

The result can be shown in multiple forms.

Exact Form:

$3 \sqrt[4]{2}$

Decimal Form:

$3.56762134 \dots$

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