If A = 8√6 - 8√5, B = 8√6 + 8√5, C = 6√6 + 6√5, D = 4√6 + 4√5, and E = √6 + √5, then which of the following…

Question

If A = 8√6 - 8√5, B = 8√6 + 8√5, C = 6√6 + 6√5, D = 4√6 + 4√5, and E = √6 + √5, then which of the following is a rational number?

Accepted Answer

Correct answer: B — Correct answer: AB Use (a - b)(a + b) = a² - b² for A × B. AB = (8√6 - 8√5)(8√6 + 8√5) = (8√6)² - (8√5)² = 384 - 320 = 64. Since 64 is rational, AB is rational. Other listed products such as CD, ABDE, and ABCDE contain radical terms like √30, so they are not rational.

Answer

A. ABDE

Answer

B. AB

Answer

C. CD

Answer

D. ABCDE

If A = 8√6 - 8√5, B = 8√6 + 8√5, C = 6√6 + 6√5, D = 4√6 + 4√5, and E = √6 +…