The Real Number Mystery: Radical Investigations
Case 1 of 5 · Jordan R. · 1A
Welcome, Radical Investigator! Every number has an identity. Some numbers can be written as fractions. Others cannot. Your mission is to uncover number identities, investigate radicals, and discover how factors work together to simplify expressions. Complete five cases to unlock your independent mastery check.
Learning objectives
- I can classify numbers as rational or irrational and explain why.
- I can identify perfect squares and perfect cubes.
- I can simplify square roots by grouping identical factors in pairs.
- I can simplify cube roots by grouping identical factors in groups of three.
- I can add, subtract, and multiply radical expressions.
- I can determine whether the result of an operation is rational or irrational.
- I can justify my mathematical thinking using examples and counterexamples.
Case 1 of 5
Number Identity
Decide whether each number is rational (it can be written as a fraction of integers) or irrational.
1 · √49
Is √49 rational or irrational?
2 · √18
Is √18 rational or irrational?
3 · 0.363636… (36 repeats forever)
Is 0.363636… (36 repeats forever) rational or irrational?
4 · ∛(−8)
Is ∛(−8) rational or irrational?