Question

Finding an irrational number between which given pair of numbers supports the idea that irrational numbers are dense inreal numbers?3.14 and pi3.33 and 1/3e^2 and √54√64/2 and √16

Answer 1

B. 3.33 and 1/3

Step-by-step explanation:

To prove that irrational numbers are dense in real numbers, we show that between any two numbers x and y there are two rational numbers, and between those two rational numbers, there is an irrational number.

In option A, pi is already irrational.

In Option C, the Euler number (e) and √54 are irrational.

In Option D, √64/2=4, and √16=4. Therefore, there cannot be any number between 4 and 4.

However, in Option B:

1/3 and 3.33 are rational numbers and they have the irrational number (pi) in between them.

Therefore, it is the pair of numbers that support the idea that irrational numbers are dense in real numbers.