Question

11.h.17b. tuesday weekly bell work-december 16th
how many irrational numbers are there between 1 and 6 ?
○ 1
○ 3
○ 4
○ 10
○ infinitely many

Explanation:

Step1: Recall irrational numbers' nature

Irrational numbers are non - repeating, non - terminating decimals. Also, between any two distinct real numbers, there are infinitely many real numbers. And among these real numbers, there are infinitely many irrational numbers.

Step2: Analyze the interval (1,6)

The interval from 1 to 6 contains infinitely many real numbers. For example, we can consider numbers like $\sqrt{2}\approx1.414...$, $\sqrt{3}\approx1.732...$, $\pi\approx3.14159...$, $\sqrt{5}\approx2.236...$, $\sqrt{6}\approx2.449...$, $\sqrt{7}\approx2.645...$ and so on. We can also create irrational numbers by adding an irrational part to a rational number in this interval, like $2 + \sqrt{2}$, $3+\pi$ (as long as the result is between 1 and 6). Since we can keep generating new irrational numbers in the interval (1,6) and there is no upper limit to the number of such numbers, the number of irrational numbers between 1 and 6 is infinitely many.

Answer:

Infinitely many