Question

Select all the expressions that represent a rational number. sqrt(169) + 7; 3 - sqrt(8); (sqrt(27))/(sqrt(3)); (sqrt(36))/(sqrt(24)); (3 + sqrt(11))/(6 + sqrt(22))

Answer 1

wrong.
√27/√3 = √9 = 3
√36/√24 = √(3/2), so no
(3 + √11)/(6 + √22) is clearly not rational

Answer 2

(sqrt(169) + 7); (sqrt(36))/(sqrt(24)); (3 + sqrt(11))/(6 + sqrt(22))

Answer 3

(sqrt(169) + 7) = 16 + 7 = 23, which is rational
3 - sqrt(8) = 3 - 2√2, which is irrational
(sqrt(27))/(sqrt(3)) = 3/√3 = 3/√3 * √3/√3 = 3√3/3 = √3, which is irrational
(sqrt(36))/(sqrt(24)) = 6/√24 = 6/(√6 * √4) = 6/(2√6) = 3/√6, which is irrational
(3 + sqrt(11))/(6 + sqrt(22)) is irrational because it involves square roots of prime numbers.