Simplify 2/5 square root of 75+1/3 square root of 27

$\frac{2}{5} \sqrt{75} + \frac{1}{3} \sqrt{27}$

Simplify each term.

Rewrite $75$ as $5^{2} \cdot 3$ .

Factor $25$ out of $75$ .

$\frac{2}{5} \cdot \sqrt{25 (3)} + \frac{1}{3} \cdot \sqrt{27}$

Rewrite $25$ as $5^{2}$ .

$\frac{2}{5} \cdot \sqrt{5^{2} \cdot 3} + \frac{1}{3} \cdot \sqrt{27}$

Pull terms out from under the radical.

$\frac{2}{5} \cdot (5 \sqrt{3}) + \frac{1}{3} \cdot \sqrt{27}$

Cancel the common factor of $5$ .

Factor $5$ out of $5 \sqrt{3}$ .

$\frac{2}{5} \cdot (5 (\sqrt{3})) + \frac{1}{3} \cdot \sqrt{27}$

Cancel the common factor.

$\frac{2}{5} \cdot (5 \sqrt{3}) + \frac{1}{3} \cdot \sqrt{27}$

Rewrite the expression.

$2 \cdot \sqrt{3} + \frac{1}{3} \cdot \sqrt{27}$

Rewrite $27$ as $3^{2} \cdot 3$ .

Factor $9$ out of $27$ .

$2 \sqrt{3} + \frac{1}{3} \cdot \sqrt{9 (3)}$

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

$2 \sqrt{3} + \frac{1}{3} \cdot \sqrt{3^{2} \cdot 3}$

Pull terms out from under the radical.

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

Cancel the common factor of $3$ .

Factor $3$ out of $3 \sqrt{3}$ .

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

Cancel the common factor.

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

Rewrite the expression.

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

Add $2 \sqrt{3}$ and $\sqrt{3}$ .

$3 \sqrt{3}$

The result can be shown in multiple forms.

Exact Form:

$3 \sqrt{3}$

Decimal Form:

$5.19615242 \dots$