Question

prove that 3+2root2 is irrational


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Answer 1

Answer:

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.

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Answer 2

Answer:

first you have to assume that it is a rational number then a and b is not equal to zero and you have to put √3= a square so √3= a square upon b square and it is 3 a square √3= b square so it is 3 b square and again √3 = c square so it is 3 c square and we know that 3 has only one has a common factor so our contraction that √ 3 is rational number is wrong hence it is irrational number this is example of prove that √ 3 is irrational number so you see this and do it yourself