Answer
$\dfrac{3\sqrt{100x^{2}}}{2\sqrt{2x^{-1}}}=\dfrac{15}{2}x\sqrt{2x}$
Work Step by Step
$\dfrac{3\sqrt{100x^{2}}}{2\sqrt{2x^{-1}}}$
Rewrite this expression as $\dfrac{3}{2}\sqrt{\dfrac{100x^{2}}{2x^{-1}}}$:
$\dfrac{3\sqrt{100x^{2}}}{2\sqrt{2x^{-1}}}=\dfrac{3}{2}\sqrt{\dfrac{100x^{2}}{2x^{-1}}}=...$
Evaluate the division inside the square root:
$...=\dfrac{3}{2}\sqrt{50x^{2+1}}=\dfrac{3}{2}\sqrt{50x^{3}}=...$
Rewrite the expression inside the square root as $25\cdot2\cdot x^{2}\cdot x$ and simplify:
$...=\dfrac{3}{2}\sqrt{25\cdot2\cdot x^{2}\cdot x}=\dfrac{3}{2}\cdot5\cdot x\sqrt{2x}=\dfrac{15}{2}x\sqrt{2x}$
