Simplify square root of (18X^3)/(49xy^2)

$\sqrt{\frac{18 X^{3}}{49 x y^{2}}}$

Step 1

Rewrite $\frac{18 X^{3}}{49 x y^{2}}$ as ${(\frac{3 X}{7 y})}^{2} \frac{2 X}{x}$ .

Factor the perfect power ${(3 X)}^{2}$ out of $18 X^{3}$ .

$\sqrt{\frac{{(3 X)}^{2} \cdot (2 X)}{49 x y^{2}}}$

Factor the perfect power ${(7 y)}^{2}$ out of $49 x y^{2}$ .

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

Rearrange the fraction $\frac{{(3 X)}^{2} \cdot (2 X)}{{(7 y)}^{2} x}$ .

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

Step 2

Pull terms out from under the radical.

$\frac{3 X}{7 y} \sqrt{\frac{2 X}{x}}$

Step 3

Rewrite $\sqrt{\frac{2 X}{x}}$ as $\frac{\sqrt{2 X}}{\sqrt{x}}$ .

$\frac{3 X}{7 y} \cdot \frac{\sqrt{2 X}}{\sqrt{x}}$

Step 4

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

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

Step 5

Combine and simplify the denominator.

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

$\frac{3 X}{7 y} \cdot \frac{\sqrt{2 X} \sqrt{x}}{\sqrt{x} \sqrt{x}}$

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

$\frac{3 X}{7 y} \cdot \frac{\sqrt{2 X} \sqrt{x}}{{\sqrt{x}}^{1} \sqrt{x}}$

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

$\frac{3 X}{7 y} \cdot \frac{\sqrt{2 X} \sqrt{x}}{{\sqrt{x}}^{1} {\sqrt{x}}^{1}}$

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

$\frac{3 X}{7 y} \cdot \frac{\sqrt{2 X} \sqrt{x}}{{\sqrt{x}}^{1 + 1}}$

Add $1$ and $1$ .

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

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

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

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

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

$\frac{3 X}{7 y} \cdot \frac{\sqrt{2 X} \sqrt{x}}{x^{\frac{1}{2} \cdot 2}}$

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

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

Cancel the common factor of $2$ .

Cancel the common factor.

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

Rewrite the expression.

$\frac{3 X}{7 y} \cdot \frac{\sqrt{2 X} \sqrt{x}}{x^{1}}$

Simplify.

$\frac{3 X}{7 y} \cdot \frac{\sqrt{2 X} \sqrt{x}}{x}$

Step 6

Combine using the product rule for radicals.

$\frac{3 X}{7 y} \cdot \frac{\sqrt{2 X x}}{x}$

Step 7

Multiply $\frac{3 X}{7 y}$ by $\frac{\sqrt{2 X x}}{x}$ .

$\frac{3 X \sqrt{2 X x}}{7 y x}$

Simplify square root of (18X^3)/(49xy^2)

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