Classify the numbers as rational or irrational:
square root of 77
square root of 48
0.375654535….
0.3757575….
- 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.
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
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.