Question

Which of the following is an irrational number between 5 and 7: 6–√, 12−−√, 27−−√, 36−−√?

Answer 1

To determine which number is irrational, we need to recall that irrational numbers cannot be expressed as fractions and do not terminate or repeat.

First, we can simplify each of the given expressions to determine if they can be expressed as fractions:

- 6–√ cannot be simplified further and does not have a rational square root.
- 12−−√ simplifies to 2√3, which can be expressed as a fraction (2√3/1).
- 27−−√ simplifies to 3√3, which can be expressed as a fraction (3√3/1).
- 36−−√ simplifies to 6, which is a rational number.

Thus, the only number that is irrational between 5 and 7 is 6–√.