Algebra Examples

$\sqrt[4]{10^{5}} \cdot \sqrt[4]{10}$

Step 1

Combine using the product rule for radicals.

$\sqrt[4]{10^{5} \cdot 10}$

Step 2

Raise $10$ to the power of $5$ .

$\sqrt[4]{100000 \cdot 10}$

Step 3

Multiply $100000$ by $10$ .

$\sqrt[4]{1000000}$

Step 4

Rewrite $1000000$ as $10^{4} \cdot 100$ .

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Step 4.1

Factor $10000$ out of $1000000$ .

$\sqrt[4]{10000 (100)}$

Step 4.2

Rewrite $10000$ as $10^{4}$ .

$\sqrt[4]{10^{4} \cdot 100}$

Step 5

Pull terms out from under the radical.

$| 10 | \sqrt[4]{100}$

Step 6

The absolute value is the distance between a number and zero. The distance between $0$ and $10$ is $10$ .

$10 \sqrt[4]{100}$

Step 7

Rewrite $100$ as $10^{2}$ .

$10 \sqrt[4]{10^{2}}$

Step 8

Rewrite $\sqrt[4]{10^{2}}$ as $\sqrt{\sqrt{10^{2}}}$ .

$10 \sqrt{\sqrt{10^{2}}}$

Step 9

Pull terms out from under the radical.

$10 \sqrt{| 10 |}$

Step 10

The absolute value is the distance between a number and zero. The distance between $0$ and $10$ is $10$ .

$10 \sqrt{10}$

Step 11

The result can be shown in multiple forms.

Exact Form:

$10 \sqrt{10}$

Decimal Form:

$31.62277660 \dots$