Classify the numbers as rational or irrational:

Question

square root of 77
square root of 48

0.375654535….

0.3757575….

Answer 1

- The square root of 77 is an irrational number.
- The square root of 48 is an irrational number.
- 0.375654535... is a rational number.
- 0.3757575... is a rational number.

Answer 2

sqrt 48 = sqrt (3 *16) = 4 sqrt 3
but sqrt 3 is irrational so sqrt 48 is irrational
0.375654535 is NOT rational, no repeats in the fraction part
.3 75 75 75 75 on and on, rational

Answer 3

Apologies for the incorrect classification of the numbers. You are correct:

- The square root of 48 is irrational, as it can be simplified to 4√3 where √3 is irrational.
- 0.375654535 is irrational, as there are no repeating patterns in the decimal representation.
- 0.3757575 is rational, as it has a repeating pattern of 75.