Question

proove 3+2
$\sqrt{5}$
is irrartional​

Answer 1

Questions should be:

• Prove that 3+2√5 is Irrational number.

ANSWER:

• 3+2√5 is an Irrational number.

GIVEN:

• Number = 3+2√5

TO PROVE:

• 3+2√5 is an Irrational number.

SOLUTION:

Let 3+2√5 be a rational number which can be expressed in the form of p/q where p and q have no other common factor than 1.

=> 3+2√5 = p/q

=> 2√5 = (p/q) -3

=> 2√5 = (p-3q)/q

=> √5 = (p-3q)/2q

Here:

• (p-3q)/2q is rational but √5 is Irrational.
• Thus our contradiction is wrong.
• 3+2√5 is an Irrational number.

NOTE:

• This method of proving an irrational number is called contradiction method.
• In this method we first contradict a fact then we prove that our supposition was wrong.