Simplify ( fourth root of 3)( square root of 2)

$(\sqrt[4]{3}) (\sqrt{2})$

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

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

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

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

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

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

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

Combine using the product rule for radicals.

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

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

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

Multiply $3$ by $4$ .

$\sqrt[4]{12}$

The result can be shown in multiple forms.

Exact Form:

$\sqrt[4]{12}$

Decimal Form:

$1.86120971 \dots$