Simplify (3 square root of 2c)/(5 square root of 10x)

$\frac{3 \sqrt{2 c}}{5 \sqrt{10 x}}$

Step 1

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

$\frac{3 \sqrt{\frac{2 c}{10 x}}}{5}$

Step 2

Cancel the common factor of $2$ and $10$ .

Factor $2$ out of $2 c$ .

$\frac{3 \sqrt{\frac{2 (c)}{10 x}}}{5}$

Cancel the common factors.

Factor $2$ out of $10 x$ .

$\frac{3 \sqrt{\frac{2 (c)}{2 (5 x)}}}{5}$

Cancel the common factor.

$\frac{3 \sqrt{\frac{2 c}{2 (5 x)}}}{5}$

Rewrite the expression.

$\frac{3 \sqrt{\frac{c}{5 x}}}{5}$

Step 3

Simplify the numerator.

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

$\frac{3 \frac{\sqrt{c}}{\sqrt{5 x}}}{5}$

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

$\frac{3 (\frac{\sqrt{c}}{\sqrt{5 x}} \cdot \frac{\sqrt{5 x}}{\sqrt{5 x}})}{5}$

Combine and simplify the denominator.

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

$\frac{3 \frac{\sqrt{c} \sqrt{5 x}}{\sqrt{5 x} \sqrt{5 x}}}{5}$

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

$\frac{3 \frac{\sqrt{c} \sqrt{5 x}}{{\sqrt{5 x}}^{1} \sqrt{5 x}}}{5}$

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

$\frac{3 \frac{\sqrt{c} \sqrt{5 x}}{{\sqrt{5 x}}^{1} {\sqrt{5 x}}^{1}}}{5}$

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

$\frac{3 \frac{\sqrt{c} \sqrt{5 x}}{{\sqrt{5 x}}^{1 + 1}}}{5}$

Add $1$ and $1$ .

$\frac{3 \frac{\sqrt{c} \sqrt{5 x}}{{\sqrt{5 x}}^{2}}}{5}$

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

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

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

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

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

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

$\frac{3 \frac{\sqrt{c} \sqrt{5 x}}{{(5 x)}^{\frac{2}{2}}}}{5}$

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{3 \frac{\sqrt{c} \sqrt{5 x}}{{(5 x)}^{\frac{2}{2}}}}{5}$

Rewrite the expression.

$\frac{3 \frac{\sqrt{c} \sqrt{5 x}}{{(5 x)}^{1}}}{5}$

Simplify.

$\frac{3 \frac{\sqrt{c} \sqrt{5 x}}{5 x}}{5}$

Combine using the product rule for radicals.

$\frac{3 \frac{\sqrt{c \cdot 5 x}}{5 x}}{5}$

Step 4

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

$\frac{\frac{3 \sqrt{c \cdot 5 x}}{5 x}}{5}$

Step 5

Move $5$ to the left of $c$ .

$\frac{\frac{3 \sqrt{5 c x}}{5 x}}{5}$

Step 6

Multiply the numerator by the reciprocal of the denominator.

$\frac{3 \sqrt{5 c x}}{5 x} \cdot \frac{1}{5}$

Step 7

Multiply $\frac{3 \sqrt{5 c x}}{5 x} \cdot \frac{1}{5}$ .

Multiply $\frac{3 \sqrt{5 c x}}{5 x}$ by $\frac{1}{5}$ .

$\frac{3 \sqrt{5 c x}}{5 x \cdot 5}$

Multiply $5$ by $5$ .

$\frac{3 \sqrt{5 c x}}{25 x}$

Simplify (3 square root of 2c)/(5 square root of 10x)

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