Question

Please include step by step instruction, so I can learn how to solve the problem. Thank you

Answer 1

9514 1404 393

Answer:

  A, C

Step-by-step explanation:

First of all, recognize that any basic arithmetic operation between a rational number and an irrational number will have an irrational result. That means, you can eliminate any answer choices that involve an irrational number.

Fractions and mixed numbers involving integers are always rational, so you only need to look at the radicals. You know 9 is 3×3, so is a perfect square, and √9 = 3 is rational. You know 5 is not a perfect square, so √5 is irrational.

Considering the above, any expression involving √5 will have an irrational result. That means you can eliminate choices B and D.

  choices A and C will result in a rational number

_____

Additional comment

  A = 6.8 +0.75 = 7.55 (rational)

  C = 6.8 × 0.75 = 5.100 (rational)