## Algebra: A Combined Approach (4th Edition)

$\dfrac{3\sqrt{100x^{2}}}{2\sqrt{2x^{-1}}}=\dfrac{15}{2}x\sqrt{2x}$
$\dfrac{3\sqrt{100x^{2}}}{2\sqrt{2x^{-1}}}$ 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: $...=\dfrac{3}{2}\sqrt{25\cdot2\cdot x^{2}\cdot x}=\dfrac{3}{2}\cdot5\cdot x\sqrt{2x}=\dfrac{15}{2}x\sqrt{2x}$