Question

Can someone tell me if I’m correct

Answer 1

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.