Question

M=sqrt2

N=sqrt5
S=2
T=5
Which expressions result in an irrational number? Select all that apply.

M+N
M*N
S+T
S*T
M*S
N+T
N^2

Answer 1

Irrational numbers are real numbers which cannot be expressed as a ration or fraction between two integers. They never repeat and go on forever without an end.

irrational number + rational number = irrational number
irrational number x rational number = irrational number

Here, M and N are irrational numbers while S and T are rational. Because,
M = √2 = 1.414213.........
N = √5 = 2.236067..........

S = 2 = 2/1
T = 5 = 5/1

So,
M + N = 3.650281...... - Irrational number
M x N = 3.162277...... - irrational number
S + T = 5 - rational number
S x T = 10 - rational number
M x S = 2.828427.......- irrational number
N + T = 7.236067.......- irrational number
N² = 5 - rational number