Answer
$\frac{x \sqrt{7z}}{7y^2z^3}$
Work Step by Step
The given expression is
$=\sqrt{\frac{4x^2}{28y^4z^5}}$
Factor as square terms.
$=\sqrt{\frac{4x^2}{4y^4z^4\cdot 7z}}$
Cancel common term.
$=\sqrt{\frac{x^2}{y^4z^4\cdot 7z}}$
Multiply by $\sqrt{\frac{7z}{7z}}$.
$=\sqrt{\frac{x^2}{y^4z^4\cdot 7z}}\cdot \sqrt{\frac{7z}{7z}}$
Use product property of square roots.
$=\sqrt{\frac{x^2\cdot 7z}{y^4z^4\cdot 7^2z^2}}$
Use quotient property of square roots.
$=\frac{\sqrt{x^2\cdot 7z}}{\sqrt{y^4z^4\cdot 7^2z^2}}$
Use product property of cube roots.
$=\frac{\sqrt{x^2} \sqrt{7z}}{\sqrt{y^4}\sqrt{z^4} \sqrt{7^2}\sqrt{z^2}}$
Simplify.
$=\frac{x \sqrt{7z}}{y^2z^2 7z}$
$=\frac{x \sqrt{7z}}{7y^2z^3}$
