Simplify ( fourth root of 18)/( square root of 6)

$\frac{\sqrt[4]{18}}{\sqrt{6}}$

Multiply $\frac{\sqrt[4]{18}}{\sqrt{6}}$ by $\frac{\sqrt{6}}{\sqrt{6}}$ .

$\frac{\sqrt[4]{18}}{\sqrt{6}} \cdot \frac{\sqrt{6}}{\sqrt{6}}$

Combine and simplify the denominator.

Multiply $\frac{\sqrt[4]{18}}{\sqrt{6}}$ by $\frac{\sqrt{6}}{\sqrt{6}}$ .

$\frac{\sqrt[4]{18} \sqrt{6}}{\sqrt{6} \sqrt{6}}$

Raise $\sqrt{6}$ to the power of $1$ .

$\frac{\sqrt[4]{18} \sqrt{6}}{{\sqrt{6}}^{1} \sqrt{6}}$

Raise $\sqrt{6}$ to the power of $1$ .

$\frac{\sqrt[4]{18} \sqrt{6}}{{\sqrt{6}}^{1} {\sqrt{6}}^{1}}$

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$\frac{\sqrt[4]{18} \sqrt{6}}{{\sqrt{6}}^{1 + 1}}$

Add $1$ and $1$ .

$\frac{\sqrt[4]{18} \sqrt{6}}{{\sqrt{6}}^{2}}$

Rewrite ${\sqrt{6}}^{2}$ as $6$ .

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{6}$ as $6^{\frac{1}{2}}$ .

$\frac{\sqrt[4]{18} \sqrt{6}}{{(6^{\frac{1}{2}})}^{2}}$

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

$\frac{\sqrt[4]{18} \sqrt{6}}{6^{\frac{1}{2} \cdot 2}}$

Combine $\frac{1}{2}$ and $2$ .

$\frac{\sqrt[4]{18} \sqrt{6}}{6^{\frac{2}{2}}}$

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{\sqrt[4]{18} \sqrt{6}}{6^{\frac{2}{2}}}$

Rewrite the expression.

$\frac{\sqrt[4]{18} \sqrt{6}}{6^{1}}$

Evaluate the exponent.

$\frac{\sqrt[4]{18} \sqrt{6}}{6}$

Simplify the numerator.

Rewrite the expression using the least common index of $4$ .

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{6}$ as $6^{\frac{1}{2}}$ .

$\frac{\sqrt[4]{18} \cdot 6^{\frac{1}{2}}}{6}$

Rewrite $6^{\frac{1}{2}}$ as $6^{\frac{2}{4}}$ .

$\frac{\sqrt[4]{18} \cdot 6^{\frac{2}{4}}}{6}$

Rewrite $6^{\frac{2}{4}}$ as $\sqrt[4]{6^{2}}$ .

$\frac{\sqrt[4]{18} \sqrt[4]{6^{2}}}{6}$

Combine using the product rule for radicals.

$\frac{\sqrt[4]{18 \cdot 6^{2}}}{6}$

Raise $6$ to the power of $2$ .

$\frac{\sqrt[4]{18 \cdot 36}}{6}$

Simplify the numerator.

Multiply $18$ by $36$ .

$\frac{\sqrt[4]{648}}{6}$

Rewrite $648$ as $3^{4} \cdot 8$ .

Factor $81$ out of $648$ .

$\frac{\sqrt[4]{81 (8)}}{6}$

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

$\frac{\sqrt[4]{3^{4} \cdot 8}}{6}$

Pull terms out from under the radical.

$\frac{3 \sqrt[4]{8}}{6}$

Cancel the common factor of $3$ and $6$ .

Factor $3$ out of $3 \sqrt[4]{8}$ .

$\frac{3 (\sqrt[4]{8})}{6}$

Cancel the common factors.

Factor $3$ out of $6$ .

$\frac{3 \sqrt[4]{8}}{3 \cdot 2}$

Cancel the common factor.

$\frac{3 \sqrt[4]{8}}{3 \cdot 2}$

Rewrite the expression.

$\frac{\sqrt[4]{8}}{2}$

The result can be shown in multiple forms.

Exact Form:

$\frac{\sqrt[4]{8}}{2}$

Decimal Form:

$0.84089641 \dots$

Simplify ( fourth root of 18)/( square root of 6)

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