Question

Proove that 5+3root2 is irrational number.

Answer 1

If possible, let us suppose that 5 + 3 root 2 is rational; then,

5 + 3 root 2 - 5 = a rational number

or, 3 root 2 = a rational number

or, (3 root 2)/3 = a rational number

or, root 2 = a rational number

This contradicts the fact that root 2 is irrational. This contradiction arises by taking 5 + 3 root 2 rational.

Hence, 5 + 3 root 2 is an irrational number.

HOPE THIS COULD HELP!!!

Answer 2

Solution:-

To Prove:-

• 5 +3 √2 is Irrational Number.

Proof:-

• Let suppose that ( 5 + 3√2 ) is a Rational Number.

So, It can be written in the form of p/q where q ≠ 0 and p & q are co-prime Numbers.

=) ( 5 + 3√2 ) = p/q

=) 3√2 = p/q - 5

=) 3√2 = ( p - 5q)/q

=) √2 = ( p - 5q)/3q________(1)

We know that,

√2 is an Irrational Number but according to our assumption ( 5 + 3√2 ) is an Irrational Number.

Rational Number can't be equal to an Irrational Number.

Hence,

Equation (1) contradicts our assumption.

=) ( 5 + 3√2 ) is an Irrational Number.

Hence Proved!