Question

Which of the following is not irrational: (3 + √7)(3 - √7)(3 - 17)?

A) (3 + √7)(3 - √7)
B) (3 - 17)
C) Both A and B
D) None of the above

Answer 1

To determine which of the given options is not irrational, we evaluate each option individually and find that neither of the options (A or B) is irrational.

Step-by-step explanation:

To determine which of the given options is not irrational, we need to evaluate each option individually. Let's start with option A: (3 + √7)(3 - √7). We can use the difference of squares formula to simplify this expression: (a + b)(a - b) = a^2 - b^2. Applying this formula, we get (3 + √7)(3 - √7) = 3^2 - (√7)^2 = 9 - 7 = 2. Since 2 is a rational number (it can be expressed as a fraction), option A is rational.

Next, let's evaluate option B: (3 - 17). Simplifying this expression, we get 3 - 17 = -14, which is a rational number. Therefore, option B is also rational.

Since both option A and option B are rational, the correct answer is C) Both A and B. Neither of the given options is irrational.