which expression is equivalent to $sqrt{\frac{2x^{5}}{18}}$? assume $xgeq0$.\n$\frac{x^{2}sqrt{x}}{3}$\n$\fra…

which expression is equivalent to $sqrt{\frac{2x^{5}}{18}}$? assume $xgeq0$.\n$\frac{x^{2}sqrt{x}}{3}$\n$\frac{3sqrt{x}}{x^{2}}$\n$\frac{sqrt{x}}{3x^{2}}$\n$\frac{2xsqrt{x}}{3}$

which expression is equivalent to $sqrt{\frac{2x^{5}}{18}}$? assume $xgeq0$.\n$\frac{x^{2}sqrt{x}}{3}$\n$\frac{3sqrt{x}}{x^{2}}$\n$\frac{sqrt{x}}{3x^{2}}$\n$\frac{2xsqrt{x}}{3}$

Answer

Explanation:

Step1: Simplify the fraction inside the square - root

Simplify $\frac{2x^{5}}{18}$ to $\frac{x^{5}}{9}$ by dividing both the numerator and denominator by 2. So we have $\sqrt{\frac{x^{5}}{9}}$.

Step2: Apply the square - root property $\sqrt{\frac{a}{b}}=\frac{\sqrt{a}}{\sqrt{b}}$

We get $\frac{\sqrt{x^{5}}}{\sqrt{9}}$. Since $\sqrt{9} = 3$, the expression becomes $\frac{\sqrt{x^{5}}}{3}$.

Step3: Rewrite $\sqrt{x^{5}}$ using exponent rules

We know that $\sqrt{x^{5}}=x^{\frac{5}{2}}=x^{2+\frac{1}{2}}=x^{2}\cdot x^{\frac{1}{2}}=x^{2}\sqrt{x}$.

Step4: Substitute the simplified $\sqrt{x^{5}}$ back

The expression is $\frac{x^{2}\sqrt{x}}{3}$.

Answer:

$\frac{x^{2}\sqrt{x}}{3}$