Evaluate square root of 54/6+2/3

$\sqrt{\frac{54}{6}} + \frac{2}{3}$

Simplify each term.

Divide $54$ by $6$ .

$\sqrt{9} + \frac{2}{3}$

Rewrite $9$ as $3^{2}$ .

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

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

$3 + \frac{2}{3}$

To write $3$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$3 \cdot \frac{3}{3} + \frac{2}{3}$

Combine $3$ and $\frac{3}{3}$ .

$\frac{3 \cdot 3}{3} + \frac{2}{3}$

Combine the numerators over the common denominator.

$\frac{3 \cdot 3 + 2}{3}$

Simplify the numerator.

Multiply $3$ by $3$ .

$\frac{9 + 2}{3}$

Add $9$ and $2$ .

$\frac{11}{3}$

The result can be shown in multiple forms.

Exact Form:

$\frac{11}{3}$

Decimal Form:

$3.\overline{6}$

Mixed Number Form:

$3 \frac{2}{3}$