Simplify ( square root of 2)/( square root of 10x)

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

Step 1

Combine $\sqrt{2}$ and $\sqrt{10 x}$ into a single radical.

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

Step 2

Reduce the expression $\frac{2}{10 x}$ by cancelling the common factors.

Factor $2$ out of $2$ .

$\sqrt{\frac{2 (1)}{10 x}}$

Factor $2$ out of $10 x$ .

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

Cancel the common factor.

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

Rewrite the expression.

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

Step 3

Rewrite $\sqrt{\frac{1}{5 x}}$ as $\frac{\sqrt{1}}{\sqrt{5 x}}$ .

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

Step 4

Any root of $1$ is $1$ .

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

Step 5

Multiply $\frac{1}{\sqrt{5 x}}$ by $\frac{\sqrt{5 x}}{\sqrt{5 x}}$ .

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

Step 6

Combine and simplify the denominator.

Multiply $\frac{1}{\sqrt{5 x}}$ by $\frac{\sqrt{5 x}}{\sqrt{5 x}}$ .

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

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

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

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

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

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

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

Add $1$ and $1$ .

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

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

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

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

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

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

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

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

Cancel the common factor of $2$ .

Cancel the common factor.

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

Rewrite the expression.

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

Simplify.

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

Simplify ( square root of 2)/( square root of 10x)

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