Simplify ( square root of 72)/3+ square root of 50

$\frac{\sqrt{72}}{3} + \sqrt{50}$

Simplify each term.

Simplify the numerator.

Rewrite $72$ as $6^{2} \cdot 2$ .

Factor $36$ out of $72$ .

$\frac{\sqrt{36 (2)}}{3} + \sqrt{50}$

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

$\frac{\sqrt{6^{2} \cdot 2}}{3} + \sqrt{50}$

$\frac{\sqrt{6^{2} \cdot 2}}{3} + \sqrt{50}$

Pull terms out from under the radical.

$\frac{6 \sqrt{2}}{3} + \sqrt{50}$

$\frac{6 \sqrt{2}}{3} + \sqrt{50}$

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

Factor $3$ out of $6 \sqrt{2}$ .

$\frac{3 (2 \sqrt{2})}{3} + \sqrt{50}$

Cancel the common factors.

Factor $3$ out of $3$ .

$\frac{3 (2 \sqrt{2})}{3 (1)} + \sqrt{50}$

Cancel the common factor.

$\frac{3 (2 \sqrt{2})}{3 \cdot 1} + \sqrt{50}$

Rewrite the expression.

$\frac{2 \sqrt{2}}{1} + \sqrt{50}$

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

$2 \sqrt{2} + \sqrt{50}$

$2 \sqrt{2} + \sqrt{50}$

$2 \sqrt{2} + \sqrt{50}$

Rewrite $50$ as $5^{2} \cdot 2$ .

Factor $25$ out of $50$ .

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

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

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

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

Pull terms out from under the radical.

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

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

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

$7 \sqrt{2}$

The result can be shown in multiple forms.

Exact Form:

$7 \sqrt{2}$

Decimal Form:

$9.89949493 \dots$

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