Question Express (2x^3)/(sqrt (36x^5)) in simplest radical form with a rational denominator (assume xgt 0 Answer Attempt 1 out of 3 square

To express $\frac {2x^{3}}{\sqrt {36x^{5}}}$ in simplest radical form with a rational denominator, we need to rationalize the denominator.<br /><br />Step 1: Rationalize the denominator by multiplying both the numerator and denominator by $\sqrt{36x^5}$.<br />$\frac {2x^{3}}{\sqrt {36x^{5}}} \times \frac {\sqrt{36x^5}}{\sqrt{36x^5}} = \frac {2x^{3}\sqrt{36x^5}}{36x^5}$<br /><br />Step 2: Simplify the numerator and denominator.<br />$\frac {2x^{3}\sqrt{36x^5}}{36x^5} = \frac {2x^{3}\cdot 6x^2}{36x^5} = \frac {12x^5}{36x^5} = \frac {1}{3}$<br /><br />Therefore, the expression $\frac {2x^{3}}{\sqrt {36x^{5}}}$ in simplest radical form with a rational denominator is $\frac {1}{3}$.