Answer:
No, you are only partially correct. Select sqrt(12)/3 and sqrt(8).
Step-by-step explanation:
An irrational number is simply a number that results in a non-repeating and non-terminating decimal. A rational number is simply any number that can be expressed as a ratio of whole numbers. Using these definitions, let's go through each answer choice:
- 1 / 3 --> Rational number since ratio of -1 to 3
0.6666 (repeating) --> Rational number since common ratio results in repeating non terminating number. In this case, 2/3.
sqrt(12) / 3 --> Irrational number since we have the ratio (2/3) times sqrt(3). The sqrt(3) is irrational itself since it cannot be expressed as a whole number ratio, and results in a non-repeating and non-terminating decimal. sqrt(12) reduces into sqrt(4 * 3) which reduces into 2sqrt(3).
(sqrt(2))^2 --> Rational number since the square root operation is negated by the square operation leaving the whole number 2.
sqrt(8) --> Irrational number since we have 2 * sqrt(2), which itself cannot be expressed as a whole number ratio, and results in a non-repeating and non-terminating decimal. sqrt(8) reduces to sqrt(4 * 2) which reduces to 2 * sqrt(2)
Hence, our two irrational numbers are sqrt(12)/3 and sqrt(8).
Cheers.
