Simplify ( square root of 20x)/9+ square root of (5x)/9

$\frac{\sqrt{20 x}}{9} + \sqrt{\frac{5 x}{9}}$

Simplify each term.

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Simplify the numerator.

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Rewrite $20 x$ as $2^{2} \cdot (5 x)$ .

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Factor $4$ out of $20$ .

$\frac{\sqrt{4 (5) x}}{9} + \sqrt{\frac{5 x}{9}}$

Rewrite $4$ as $2^{2}$ .

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

Add parentheses.

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

Pull terms out from under the radical.

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

Rewrite $\frac{5 x}{9}$ as ${(\frac{1}{3})}^{2} (5 x)$ .

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Factor the perfect power $1^{2}$ out of $5 x$ .

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

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

$\frac{2 \sqrt{5 x}}{9} + \sqrt{\frac{1^{2} (5 x)}{3^{2} \cdot 1}}$

Rearrange the fraction $\frac{1^{2} (5 x)}{3^{2} \cdot 1}$ .

$\frac{2 \sqrt{5 x}}{9} + \sqrt{{(\frac{1}{3})}^{2} (5 x)}$

Pull terms out from under the radical.

$\frac{2 \sqrt{5 x}}{9} + \frac{1}{3} \sqrt{5 x}$

Combine $\frac{1}{3}$ and $\sqrt{5 x}$ .

$\frac{2 \sqrt{5 x}}{9} + \frac{\sqrt{5 x}}{3}$

To write $\frac{\sqrt{5 x}}{3}$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$\frac{2 \sqrt{5 x}}{9} + \frac{\sqrt{5 x}}{3} \cdot \frac{3}{3}$

Write each expression with a common denominator of $9$ , by multiplying each by an appropriate factor of $1$ .

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Multiply $\frac{\sqrt{5 x}}{3}$ and $\frac{3}{3}$ .

$\frac{2 \sqrt{5 x}}{9} + \frac{\sqrt{5 x} \cdot 3}{3 \cdot 3}$

Multiply $3$ by $3$ .

$\frac{2 \sqrt{5 x}}{9} + \frac{\sqrt{5 x} \cdot 3}{9}$

Combine the numerators over the common denominator.

$\frac{2 \sqrt{5 x} + \sqrt{5 x} \cdot 3}{9}$

Simplify the numerator.

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Move $3$ to the left of $\sqrt{5 x}$ .

$\frac{2 \sqrt{5 x} + 3 \cdot \sqrt{5 x}}{9}$

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

$\frac{5 \sqrt{5 x}}{9}$

Simplify ( square root of 20x)/9+ square root of (5x)/9

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