Simplify square root of (7x^8y^4)/(6x^6y)

$\sqrt{\frac{7 x^{8} y^{4}}{6 x^{6} y}}$

Reduce the expression $\frac{7 x^{8} y^{4}}{6 x^{6} y}$ by cancelling the common factors.

Factor $x^{6}$ out of $7 x^{8} y^{4}$ .

$\sqrt{\frac{x^{6} (7 x^{2} y^{4})}{6 x^{6} y}}$

Factor $x^{6}$ out of $6 x^{6} y$ .

$\sqrt{\frac{x^{6} (7 x^{2} y^{4})}{x^{6} (6 y)}}$

Cancel the common factor.

$\sqrt{\frac{x^{6} (7 x^{2} y^{4})}{x^{6} (6 y)}}$

Rewrite the expression.

$\sqrt{\frac{7 x^{2} y^{4}}{6 y}}$

Cancel the common factor of $y^{4}$ and $y$ .

Factor $y$ out of $7 x^{2} y^{4}$ .

$\sqrt{\frac{y (7 x^{2} y^{3})}{6 y}}$

Cancel the common factors.

Factor $y$ out of $6 y$ .

$\sqrt{\frac{y (7 x^{2} y^{3})}{y \cdot 6}}$

Cancel the common factor.

$\sqrt{\frac{y (7 x^{2} y^{3})}{y \cdot 6}}$

Rewrite the expression.

$\sqrt{\frac{7 x^{2} y^{3}}{6}}$

Rewrite $\sqrt{\frac{7 x^{2} y^{3}}{6}}$ as $\frac{\sqrt{7 x^{2} y^{3}}}{\sqrt{6}}$ .

$\frac{\sqrt{7 x^{2} y^{3}}}{\sqrt{6}}$

Simplify the numerator.

Rewrite $7 x^{2} y^{3}$ as ${(x y)}^{2} \cdot (7 y)$ .

Factor out $y^{2}$ .

$\frac{\sqrt{7 x^{2} (y^{2} y)}}{\sqrt{6}}$

Move $7$ .

$\frac{\sqrt{x^{2} y^{2} \cdot 7 y}}{\sqrt{6}}$

Rewrite $x^{2} y^{2}$ as ${(x y)}^{2}$ .

$\frac{\sqrt{{(x y)}^{2} \cdot 7 y}}{\sqrt{6}}$

Add parentheses.

$\frac{\sqrt{{(x y)}^{2} \cdot (7 y)}}{\sqrt{6}}$

Pull terms out from under the radical.

$\frac{x y \sqrt{7 y}}{\sqrt{6}}$

Multiply $\frac{x y \sqrt{7 y}}{\sqrt{6}}$ by $\frac{\sqrt{6}}{\sqrt{6}}$ .

$\frac{x y \sqrt{7 y}}{\sqrt{6}} \cdot \frac{\sqrt{6}}{\sqrt{6}}$

Combine and simplify the denominator.

Multiply $\frac{x y \sqrt{7 y}}{\sqrt{6}}$ by $\frac{\sqrt{6}}{\sqrt{6}}$ .

$\frac{x y \sqrt{7 y} \sqrt{6}}{\sqrt{6} \sqrt{6}}$

Raise $\sqrt{6}$ to the power of $1$ .

$\frac{x y \sqrt{7 y} \sqrt{6}}{{\sqrt{6}}^{1} \sqrt{6}}$

Raise $\sqrt{6}$ to the power of $1$ .

$\frac{x y \sqrt{7 y} \sqrt{6}}{{\sqrt{6}}^{1} {\sqrt{6}}^{1}}$

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

$\frac{x y \sqrt{7 y} \sqrt{6}}{{\sqrt{6}}^{1 + 1}}$

Add $1$ and $1$ .

$\frac{x y \sqrt{7 y} \sqrt{6}}{{\sqrt{6}}^{2}}$

Rewrite ${\sqrt{6}}^{2}$ as $6$ .

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{6}$ as $6^{\frac{1}{2}}$ .

$\frac{x y \sqrt{7 y} \sqrt{6}}{{(6^{\frac{1}{2}})}^{2}}$

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

$\frac{x y \sqrt{7 y} \sqrt{6}}{6^{\frac{1}{2} \cdot 2}}$

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

$\frac{x y \sqrt{7 y} \sqrt{6}}{6^{\frac{2}{2}}}$

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{x y \sqrt{7 y} \sqrt{6}}{6^{\frac{2}{2}}}$

Rewrite the expression.

$\frac{x y \sqrt{7 y} \sqrt{6}}{6^{1}}$

Evaluate the exponent.

$\frac{x y \sqrt{7 y} \sqrt{6}}{6}$

Simplify the numerator.

Combine using the product rule for radicals.

$\frac{x y \sqrt{6 (7 y)}}{6}$

Multiply $6$ by $7$ .

$\frac{x y \sqrt{42 y}}{6}$

Simplify square root of (7x^8y^4)/(6x^6y)

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