Simplify the Radical Expression square root of (3x^2)/(7x^3)

$\sqrt{\frac{3 x^{2}}{7 x^{3}}}$

Step 1

Reduce the expression $\frac{3 x^{2}}{7 x^{3}}$ by cancelling the common factors.

Factor $x^{2}$ out of $3 x^{2}$ .

$\sqrt{\frac{x^{2} \cdot 3}{7 x^{3}}}$

Factor $x^{2}$ out of $7 x^{3}$ .

$\sqrt{\frac{x^{2} \cdot 3}{x^{2} (7 x)}}$

Cancel the common factor.

$\sqrt{\frac{x^{2} \cdot 3}{x^{2} (7 x)}}$

Rewrite the expression.

$\sqrt{\frac{3}{7 x}}$

Step 2

Rewrite $\sqrt{\frac{3}{7 x}}$ as $\frac{\sqrt{3}}{\sqrt{7 x}}$ .

$\frac{\sqrt{3}}{\sqrt{7 x}}$

Step 3

Multiply $\frac{\sqrt{3}}{\sqrt{7 x}}$ by $\frac{\sqrt{7 x}}{\sqrt{7 x}}$ .

$\frac{\sqrt{3}}{\sqrt{7 x}} \cdot \frac{\sqrt{7 x}}{\sqrt{7 x}}$

Step 4

Combine and simplify the denominator.

Multiply $\frac{\sqrt{3}}{\sqrt{7 x}}$ by $\frac{\sqrt{7 x}}{\sqrt{7 x}}$ .

$\frac{\sqrt{3} \sqrt{7 x}}{\sqrt{7 x} \sqrt{7 x}}$

Raise $\sqrt{7 x}$ to the power of $1$ .

$\frac{\sqrt{3} \sqrt{7 x}}{{\sqrt{7 x}}^{1} \sqrt{7 x}}$

Raise $\sqrt{7 x}$ to the power of $1$ .

$\frac{\sqrt{3} \sqrt{7 x}}{{\sqrt{7 x}}^{1} {\sqrt{7 x}}^{1}}$

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

$\frac{\sqrt{3} \sqrt{7 x}}{{\sqrt{7 x}}^{1 + 1}}$

Add $1$ and $1$ .

$\frac{\sqrt{3} \sqrt{7 x}}{{\sqrt{7 x}}^{2}}$

Rewrite ${\sqrt{7 x}}^{2}$ as $7 x$ .

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{7 x}$ as ${(7 x)}^{\frac{1}{2}}$ .

$\frac{\sqrt{3} \sqrt{7 x}}{{({(7 x)}^{\frac{1}{2}})}^{2}}$

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

$\frac{\sqrt{3} \sqrt{7 x}}{{(7 x)}^{\frac{1}{2} \cdot 2}}$

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

$\frac{\sqrt{3} \sqrt{7 x}}{{(7 x)}^{\frac{2}{2}}}$

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{\sqrt{3} \sqrt{7 x}}{{(7 x)}^{\frac{2}{2}}}$

Rewrite the expression.

$\frac{\sqrt{3} \sqrt{7 x}}{{(7 x)}^{1}}$

Simplify.

$\frac{\sqrt{3} \sqrt{7 x}}{7 x}$

Step 5

Simplify the numerator.

Combine using the product rule for radicals.

$\frac{\sqrt{3 (7 x)}}{7 x}$

Multiply $3$ by $7$ .

$\frac{\sqrt{21 x}}{7 x}$

Simplify the Radical Expression square root of (3x^2)/(7x^3)

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