Simplify ( square root of 108)/3+ square root of 75

$\frac{\sqrt{108}}{3} + \sqrt{75}$

Simplify each term.

Simplify the numerator.

Rewrite $108$ as $6^{2} \cdot 3$ .

Factor $36$ out of $108$ .

$\frac{\sqrt{36 (3)}}{3} + \sqrt{75}$

Rewrite $36$ as $6^{2}$ .

$\frac{\sqrt{6^{2} \cdot 3}}{3} + \sqrt{75}$

$\frac{\sqrt{6^{2} \cdot 3}}{3} + \sqrt{75}$

Pull terms out from under the radical.

$\frac{6 \sqrt{3}}{3} + \sqrt{75}$

$\frac{6 \sqrt{3}}{3} + \sqrt{75}$

Cancel the common factor of $6$ and $3$ .

Factor $3$ out of $6 \sqrt{3}$ .

$\frac{3 (2 \sqrt{3})}{3} + \sqrt{75}$

Cancel the common factors.

Factor $3$ out of $3$ .

$\frac{3 (2 \sqrt{3})}{3 (1)} + \sqrt{75}$

Cancel the common factor.

$\frac{3 (2 \sqrt{3})}{3 \cdot 1} + \sqrt{75}$

Rewrite the expression.

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

Divide $2 \sqrt{3}$ by $1$ .

$2 \sqrt{3} + \sqrt{75}$

$2 \sqrt{3} + \sqrt{75}$

$2 \sqrt{3} + \sqrt{75}$

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

Factor $25$ out of $75$ .

$2 \sqrt{3} + \sqrt{25 (3)}$

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

$2 \sqrt{3} + \sqrt{5^{2} \cdot 3}$

$2 \sqrt{3} + \sqrt{5^{2} \cdot 3}$

Pull terms out from under the radical.

$2 \sqrt{3} + 5 \sqrt{3}$

$2 \sqrt{3} + 5 \sqrt{3}$

Add $2 \sqrt{3}$ and $5 \sqrt{3}$ .

$7 \sqrt{3}$

The result can be shown in multiple forms.

Exact Form:

$7 \sqrt{3}$

Decimal Form:

$12.12435565 \dots$

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