Question

prove that 7-2root5 is irrational no.

Answer 1

Let us assume that 7-2√5 is rational number.
then,
7-(7-2√5) is rational {difference between two rational no. always rational}.
7-7-2√5 is rational.
-2√5 is rational.
1/-2×(-2√5) is rational {division between two rational no. always rational}.
√5 is rational.
But we know that √5 is irrational,
hence our assumption is wrong.
so,
we can say that 7-2√5 is irrational.