Simplify the Radical Expression square root of (8x)/5

$\sqrt{\frac{8 x}{5}}$

Rewrite $\sqrt{\frac{8 x}{5}}$ as $\frac{\sqrt{8 x}}{\sqrt{5}}$ .

$\frac{\sqrt{8 x}}{\sqrt{5}}$

Simplify the numerator.

Rewrite $8 x$ as $2^{2} \cdot (2 x)$ .

Factor $4$ out of $8$ .

$\frac{\sqrt{4 (2) x}}{\sqrt{5}}$

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

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

Add parentheses.

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

Pull terms out from under the radical.

$\frac{| 2 | \sqrt{2 x}}{\sqrt{5}}$

The absolute value is the distance between a number and zero. The distance between $0$ and $2$ is $2$ .

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

Multiply $\frac{2 \sqrt{2 x}}{\sqrt{5}}$ by $\frac{\sqrt{5}}{\sqrt{5}}$ .

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

Combine and simplify the denominator.

Multiply $\frac{2 \sqrt{2 x}}{\sqrt{5}}$ by $\frac{\sqrt{5}}{\sqrt{5}}$ .

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

Raise $\sqrt{5}$ to the power of $1$ .

$\frac{2 \sqrt{2 x} \sqrt{5}}{{\sqrt{5}}^{1} \sqrt{5}}$

Raise $\sqrt{5}$ to the power of $1$ .

$\frac{2 \sqrt{2 x} \sqrt{5}}{{\sqrt{5}}^{1} {\sqrt{5}}^{1}}$

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

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

Add $1$ and $1$ .

$\frac{2 \sqrt{2 x} \sqrt{5}}{{\sqrt{5}}^{2}}$

Rewrite ${\sqrt{5}}^{2}$ as $5$ .

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{5}$ as $5^{\frac{1}{2}}$ .

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

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

$\frac{2 \sqrt{2 x} \sqrt{5}}{5^{\frac{1}{2} \cdot 2}}$

Combine $\frac{1}{2}$ and $2$ .

$\frac{2 \sqrt{2 x} \sqrt{5}}{5^{\frac{2}{2}}}$

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{2 \sqrt{2 x} \sqrt{5}}{5^{\frac{2}{2}}}$

Rewrite the expression.

$\frac{2 \sqrt{2 x} \sqrt{5}}{5^{1}}$

Evaluate the exponent.

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

Simplify the numerator.

Combine using the product rule for radicals.

$\frac{2 \sqrt{5 (2 x)}}{5}$

Multiply $5$ by $2$ .

$\frac{2 \sqrt{10 x}}{5}$

Simplify the Radical Expression square root of (8x)/5

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