Trigonometry Examples

$\sqrt[4]{4} \sqrt[6]{98}$

Step 1

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

$\sqrt[4]{2^{2}} \sqrt[6]{98}$

Step 2

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

$\sqrt{\sqrt{2^{2}}} \sqrt[6]{98}$

Step 3

Pull terms out from under the radical, assuming positive real numbers.

$\sqrt{2} \sqrt[6]{98}$

Step 4

Multiply $\sqrt{2} \sqrt[6]{98}$ .

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Step 4.1

Rewrite the expression using the least common index of $6$ .

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Step 4.1.1

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{2}$ as $2^{\frac{1}{2}}$ .

$2^{\frac{1}{2}} \sqrt[6]{98}$

Step 4.1.2

Rewrite $2^{\frac{1}{2}}$ as $2^{\frac{3}{6}}$ .

$2^{\frac{3}{6}} \sqrt[6]{98}$

Step 4.1.3

Rewrite $2^{\frac{3}{6}}$ as $\sqrt[6]{2^{3}}$ .

$\sqrt[6]{2^{3}} \sqrt[6]{98}$

Step 4.2

Combine using the product rule for radicals.

$\sqrt[6]{2^{3} \cdot 98}$

Step 4.3

Raise $2$ to the power of $3$ .

$\sqrt[6]{8 \cdot 98}$

Step 4.4

Multiply $8$ by $98$ .

$\sqrt[6]{784}$

Step 5

Rewrite $784$ as $28^{2}$ .

$\sqrt[6]{28^{2}}$

Step 6

Rewrite $\sqrt[6]{28^{2}}$ as $\sqrt[3]{\sqrt{28^{2}}}$ .

$\sqrt[3]{\sqrt{28^{2}}}$

Step 7

Pull terms out from under the radical, assuming positive real numbers.

$\sqrt[3]{28}$

Step 8

The result can be shown in multiple forms.

Exact Form:

$\sqrt[3]{28}$

Decimal Form:

$3.03658897 \dots$