Real numbers
Answers are for parents and teachers.
1
Which of these are irrational: √81, √82, ∛125, ∛126, 0.454545…?
√82 and ∛126 are irrational. √81 = 9, ∛125 = 5 and 0.4545… = 5/11 are rational.
2
Write 0.555… as a fraction.
Let x = 0.555…. Then 10x − x = 5, so x = 5/9.
3
Between which two whole numbers is √90, and what is it to one decimal place?
81 < 90 < 100, so 9 < √90 < 10. 9.4² = 88.36 and 9.5² = 90.25, so √90 is between 9.4 and 9.5. 9.45² = 89.3025 is below 90, so √90 ≈ 9.5.
4
Put in order, smallest first: √3, 1.7, 7/4, √2.
Squares: 3, 2.89, 3.0625, 2. So √2 < 1.7 < √3 < 7/4.
5
Solve x² = 10 in R, and give the solution set in Q.
x = √10 or x = −√10, so the set is {√10, −√10} in R. In Q it is ∅, because √10 is irrational.