Question

I'm having problems with online school where the teacher's don't help the online students but only helps the face-to-face studentAny help would be appreciated

Answer 1

The irrational numbers are the ones that can not be expressed as a fraction of two integers.

For example, pi or the square root of 2 are irrational numbers.

In set a, we have pi, that is irrational.

In set b, we have the square root of 80, that is a multiple of the square root of 5:

`\sqrt[]{80}=\sqrt[]{16\cdot5}=\sqrt[]{16}\cdot\sqrt[]{5}=4\sqrt[]{5}`

As the square root of 5 is irrational, then their multiples are also irrational.

In set c, we have the square root of 100, that have a rational solution.

`\sqrt[]{100}=10`

In set d, we have a periodic number. The periodic numbers, although having infinite decimals, can be expressed as fractions, so they are rational.

This set has all rational numbers.

Answers: set d and set c.