Question

Prove 2root3_root5is irrational number​

Answer 1

Answer:

2√3-√5

Step-by-step explanation:

=Assume that 2√3-√5 is a rational number

=2√3-√5=p/q

=(2√3-√5)^=(p/q) ^

=(2√3)^-(√5)^=p^/q^

=2•3-5=p^/q^

=6-5=p^/q^

=1=p^/q^

Transfer p^ from rhs to Lhs

P^=1q^----------{1}

1 divides p^

P^ divides 1

From 1

1q^=1k^

Q^=1k^----------{2}

So, q divides 1

From 1 and 2

Our assumption wrong

Its a contradiction

2√3-√5 is a irrational number