Question

show that reciprocal of 3+2√2 is an irrational number​

Answer 1

Answer:

Given : Reciprocal of 3 + 2√2 i.e.,

To prove : Reciprocal of 3 + 2√2 is an irrational number.

Proof :

First of all, rationalise the denominator of the reciprocal of 3 + 2√2.

After rationalising its denominator, we get ( 3 - 2√2 ) as a result.

Now, let us assume that ( 3 - 2√2 ) is an irrational number. So, taking a rational number i.e., 3 and subtracting from it.

We have ;

[ 3 - 2√2 - 3 ]

⇒ - 2√2

As a result, we get ( - 2√2 ) which is an irrational number.

Hence, the reciprocal of ( 3 + 2√2) is an irrational number.

Answer 2

Answer:

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