Algebra Examples

$- 3 \sqrt[4]{10} \cdot 3 \sqrt[4]{500}$

Step 1

Multiply $- 3 \sqrt[4]{10} (3 \sqrt[4]{500})$ .

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Step 1.1

Multiply $3$ by $- 3$ .

$- 9 \sqrt[4]{10} \sqrt[4]{500}$

Step 1.2

Combine using the product rule for radicals.

$- 9 \sqrt[4]{500 \cdot 10}$

Step 1.3

Multiply $500$ by $10$ .

$- 9 \sqrt[4]{5000}$

$- 9 \sqrt[4]{5000}$

Step 2

Rewrite $5000$ as $5^{4} \cdot 8$ .

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Step 2.1

Factor $625$ out of $5000$ .

$- 9 \sqrt[4]{625 (8)}$

Step 2.2

Rewrite $625$ as $5^{4}$ .

$- 9 \sqrt[4]{5^{4} \cdot 8}$

$- 9 \sqrt[4]{5^{4} \cdot 8}$

Step 3

Pull terms out from under the radical.

$- 9 (5 \sqrt[4]{8})$

Step 4

Multiply $5$ by $- 9$ .

$- 45 \sqrt[4]{8}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$- 45 \sqrt[4]{8}$

Decimal Form:

$- 75.68067737 \dots$

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