Which choices if multiplied by sqrt (36) would result in an irrational number answer?Choose two. A . -(5)/(2) B 2.828427 ... C 3.454545... D sqrt (18) E sqrt ((9)/(16))

To determine which choices, when multiplied by $\sqrt{36}$, would result in an irrational number, we need to analyze each option.<br /><br />A. $-\frac{5}{2}$<br />Multiplying $-\frac{5}{2}$ by $\sqrt{36}$ gives $-\frac{5}{2} \times 6 = -15$, which is a rational number.<br /><br />B. 2.828427...<br />Multiplying 2.828427... by $\sqrt{36}$ gives 2.828427... $\times 6 = 16.9707$, which is a rational number.<br /><br />C. 3.454545...<br />Multiplying 3.454545... by $\sqrt{36}$ gives 3.454545... $\times 6 = 20.72727$, which is a rational number.<br /><br />D. $\sqrt{18}$<br />Multiplying $\sqrt{18}$ by $\sqrt{36}$ gives $\sqrt{18} \times 6 = 6\sqrt{18}$, which is an irrational number.<br /><br />E. $\sqrt{\frac{9}{16}}$<br />Multiplying $\sqrt{\frac{9}{16}}$ by $\sqrt{36}$ gives $\sqrt{\frac{9}{16}} \times 6 = \frac{3}{4} \times 6 = \frac{18}{4} = \frac{9}{2}$, which is a rational number.<br /><br />Therefore, the correct choices are D. $\sqrt{18}$ and E. $\sqrt{\frac{9}{16}}$.