Question

Which expressions result in an irrational number? Select all that apply

Answer 1

The answers are: M+N/M*N/M*S/N+T

Answer 2

M+N, M.N, M.S, N+T are irrational numbers.

Explanation:

Given

`M=\sqrt2,\\ N=\sqrt5, \\S=2, \\T=5`

we have to select irrational number from

M+N, M.N, S+T, S.T, M.S, N+T,
`N^2`

`M+N=\sqrt2+\sqrt5 \thinspace(irrational)\\\\M.N=(\sqrt2)(\sqrt5)=√(10)\thinspace(irrational)\\\\S+T=2+5=7\thinspace (rational)\\\\S.T=2.(5)=10\thinspace(rational)\\\\M.S=(\sqrt2)2=2\sqrt2\thinspace(irrational)\\\\N+T=\sqrt5+5\thinspace (irrational)\\\\N^2=(\sqrt5)^2=5\thinspace(rational)`

Hence, M+N, M.N, M.S, N+T are irrational numbers.