Distinguish rational from irrational numbers, represent them on the number line, and simplify surds.
A rational number can be written as p/q where p and q are integers and qโ 0. An irrational number cannot be expressed this way โ its decimal expansion is non-terminating and non-repeating.
Is โ16 rational or irrational?
โ16=4, which is rational since it's a whole number
Is โ7 rational or irrational?
Irrational, since 7 is not a perfect square and its decimal expansion never terminates or repeats
Is 0.333... (recurring) rational or irrational?
Rational, since it equals 1/3 exactly, a ratio of two integers
A surd is an irrational root that can't be simplified to remove the root entirely. Surds can be simplified by factoring out perfect square factors.
Simplify โ50.
โ50=โ(25ร2)=5โ2
Simplify โ72.
โ72=โ(36ร2)=6โ2
Simplify โ200.
โ200=โ(100ร2)=10โ2
1. Is โ25 rational or irrational?
2. Is ฯ rational or irrational?
3. Simplify โ48.
4. Simplify โ98.
5. Rationalize the denominator: 1/โ3
6. Is โ36 rational or irrational?
7. Is 0.1010010001... (non-repeating) rational or irrational?
8. Simplify โ125.
9. Simplify โ180.
10. Rationalize the denominator: 5/โ5