Question

Which of the following will result in a rational number? Select all that apply.

A. 7(3)/(4)-(\sqrt(11))/(5)
B. 7(3)/(4)-:(\sqrt(11))/(5)
C. 7(3)/(4)+(\sqrt(16))/(5)
D. 7(3)/(4)\times (\sqrt(16))/(5)

Answer 1

Options A, C, and D will result in rational numbers.

Step-by-step explanation:

To determine which of the given options will result in a rational number, we need to simplify each expression and check if the denominator is a non-zero integer.

1. Option A: 7(3)/(4)-(√11)/(5) = 21/4 - (√11)/(5) = (21 - 4(√11))/(4 * 5) = (21 - 4(√11))/20. Rational.
2. Option B: 7(3)/(4)-:(√11)/(5) = (7(3)/(4)) * (5/(√11)) = (21/4) * (5/(√11)) = (525/4) * (1/(√11)) = 525/(4(√11)). Not rational.
3. Option C: 7(3)/(4)+(√16)/(5) = 21/4 + 4/5 = (21 * 5 + 4 * 4)/(4 * 5) = (105 + 16)/20 = 121/20. Rational.
4. Option D: 7(3)/(4)×(√16)/(5) = 21/4 × 4/5 = (21 × 4)/(4 × 5) = 21/5. Rational.

So, options A, C, and D will result in rational numbers.