Simplify ( square root of 16)/(3 square root of 2)

$\frac{\sqrt{16}}{3 \sqrt{2}}$

Combine $\sqrt{16}$ and $\sqrt{2}$ into a single radical.

$\frac{\sqrt{\frac{16}{2}}}{3}$

Cancel the common factor of $16$ and $2$ .

Factor $2$ out of $16$ .

$\frac{\sqrt{\frac{2 \cdot 8}{2}}}{3}$

Cancel the common factors.

Factor $2$ out of $2$ .

$\frac{\sqrt{\frac{2 \cdot 8}{2 (1)}}}{3}$

Cancel the common factor.

$\frac{\sqrt{\frac{2 \cdot 8}{2 \cdot 1}}}{3}$

Rewrite the expression.

$\frac{\sqrt{\frac{8}{1}}}{3}$

Divide $8$ by $1$ .

$\frac{\sqrt{8}}{3}$

Simplify the numerator.

Rewrite $8$ as $2^{2} \cdot 2$ .

Factor $4$ out of $8$ .

$\frac{\sqrt{4 (2)}}{3}$

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

$\frac{\sqrt{2^{2} \cdot 2}}{3}$

Pull terms out from under the radical.

$\frac{2 \sqrt{2}}{3}$

The result can be shown in multiple forms.

Exact Form:

$\frac{2 \sqrt{2}}{3}$

Decimal Form:

$0.94280904 \dots$