Answer:
A, B, E are irrational
Explanation:
You want to know which expressions result in an irrational number from the given expressions involving rational and irrational numbers.
A. M+N
M + N = √2 +√5 . . . . irrational
B. MN
MN = (√2)(√5) = 10 . . . . irrational
C. S+T
S + T = 2 + 5 = 7 . . . . rational
D. ST
ST = 2·5 = 10 . . . . rational
E. N+T
N + T = √5 + 5 . . . . irrational
F. N²
N² = (√5)(√5) = 5 . . . . rational
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Additional comment
When in doubt, you can use your calculator to evaluate these expressions. If the decimal fraction uses all available digits, the number is likely irrational.
If the number cannot be expressed exactly without using symbols (√, ∛, π, e), then it is irrational. The attached calculator display shows this nicely.