Simplify ( square root of 50x)/6+ square root of (2x)/9

$\frac{\sqrt{50 x}}{6} + \sqrt{\frac{2 x}{9}}$

Step 1

Simplify each term.

Simplify the numerator.

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

Factor $25$ out of $50$ .

$\frac{\sqrt{25 (2) x}}{6} + \sqrt{\frac{2 x}{9}}$

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

$\frac{\sqrt{5^{2} \cdot 2 x}}{6} + \sqrt{\frac{2 x}{9}}$

Add parentheses.

$\frac{\sqrt{5^{2} \cdot (2 x)}}{6} + \sqrt{\frac{2 x}{9}}$

Pull terms out from under the radical.

$\frac{5 \sqrt{2 x}}{6} + \sqrt{\frac{2 x}{9}}$

Rewrite $\frac{2 x}{9}$ as ${(\frac{1}{3})}^{2} (2 x)$ .

Factor the perfect power $1^{2}$ out of $2 x$ .

$\frac{5 \sqrt{2 x}}{6} + \sqrt{\frac{1^{2} (2 x)}{9}}$

Factor the perfect power $3^{2}$ out of $9$ .

$\frac{5 \sqrt{2 x}}{6} + \sqrt{\frac{1^{2} (2 x)}{3^{2} \cdot 1}}$

Rearrange the fraction $\frac{1^{2} (2 x)}{3^{2} \cdot 1}$ .

$\frac{5 \sqrt{2 x}}{6} + \sqrt{{(\frac{1}{3})}^{2} (2 x)}$

Pull terms out from under the radical.

$\frac{5 \sqrt{2 x}}{6} + \frac{1}{3} \sqrt{2 x}$

Combine $\frac{1}{3}$ and $\sqrt{2 x}$ .

$\frac{5 \sqrt{2 x}}{6} + \frac{\sqrt{2 x}}{3}$

Step 2

To write $\frac{\sqrt{2 x}}{3}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$\frac{5 \sqrt{2 x}}{6} + \frac{\sqrt{2 x}}{3} \cdot \frac{2}{2}$

Step 3

Write each expression with a common denominator of $6$ , by multiplying each by an appropriate factor of $1$ .

Multiply $\frac{\sqrt{2 x}}{3}$ by $\frac{2}{2}$ .

$\frac{5 \sqrt{2 x}}{6} + \frac{\sqrt{2 x} \cdot 2}{3 \cdot 2}$

Multiply $3$ by $2$ .

$\frac{5 \sqrt{2 x}}{6} + \frac{\sqrt{2 x} \cdot 2}{6}$

Step 4

Combine the numerators over the common denominator.

$\frac{5 \sqrt{2 x} + \sqrt{2 x} \cdot 2}{6}$

Step 5

Simplify the numerator.

Move $2$ to the left of $\sqrt{2 x}$ .

$\frac{5 \sqrt{2 x} + 2 \cdot \sqrt{2 x}}{6}$

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

$\frac{7 \sqrt{2 x}}{6}$