Evaluate fourth root of 2* square root of 3

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

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

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{3}$ as $3^{\frac{1}{2}}$ .

$\sqrt[4]{2} \cdot 3^{\frac{1}{2}}$

Rewrite $3^{\frac{1}{2}}$ as $3^{\frac{2}{4}}$ .

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

Rewrite $3^{\frac{2}{4}}$ as $\sqrt[4]{3^{2}}$ .

$\sqrt[4]{2} \sqrt[4]{3^{2}}$

Combine using the product rule for radicals.

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

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

$\sqrt[4]{2 \cdot 9}$

Multiply $2$ by $9$ .

$\sqrt[4]{18}$

The result can be shown in multiple forms.

Exact Form:

$\sqrt[4]{18}$

Decimal Form:

$2.05976714 \dots$