Question

Select all expressions that are rational numbers.A. (3√5)+(2√5)B(3√5)-(2√5)C. (3√5) × (2√5)D. (3√5)÷ (2√5)E. (2√5)- (3√5)F.(2√5)÷ (3√5)

Answer 1

Rational numbers are numbers that are expressed as the ratio of two integers, where the denominator should not be equal to zero.

Lets check for option A

$(3\sqrt[]{5})\text{ + (2}\sqrt[]{5}\text{) = 5}\sqrt[]{5}$

Hence is not a rational number

Let's check for option B

$\begin{gathered} (3\sqrt[]{5})\text{ - (2}\sqrt[]{5}\text{) = 1}\sqrt[]{5} \\ \Rightarrow\sqrt[]{5} \end{gathered}$

option B is not a rational number

Let's check for option C

$\begin{gathered} (3\sqrt[]{5})\text{ x (2}\sqrt[]{5}\text{) = 3 x 2 x 5} \\ \Rightarrow\text{ 6 x 5 } \\ \Rightarrow\text{ 30} \end{gathered}$

Option C is a rational number

Let's check for option D

$\frac{(3\sqrt[]{5})}{(2\sqrt[]{5})}=\frac{3}{2}$

Hence option D is a rational number

Let's check for option E

$(2\sqrt[]{5})\text{ -(3}\sqrt[]{5}\text{) = -1}\sqrt[]{5}$

Option E is not a rational number

Option F

$\frac{2\sqrt[]{5}}{3\sqrt[]{5}}\text{ = }\frac{2}{3}$

Option F is a rational number