Question

show that (√3-√2) is a irrational​

Answer 1

Answer:

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let √3 - √2 = (a/b) is a rational no.

On squaring both sides , we get

2 + 3 - 2√6 = (a2/b2)

So,5 - 2√6 = (a2/b2) a rational no.

So, 2√6 = 5- (a2/b2)

Since, 2√6 is an irrational no. and 5 - (a2/b2) is a rational no.

So, my contradiction is wrong.

So, (√3 - √2) is an irrational no.

Answer 2

Answer:

let us assume the contrary that root 3 -root 2 is a rational number.

so that,

root 3- root 2 = a/b [ Where a and b has no common factor other than 1 ]

root 3 - a/b = root 2

squaring both sides

using the formula (a+b)2 = a2+ 2ab + b2

after that the value comes .

Then that is an integer and rational number.

But this contrary fact arises because of our incorrect assumption.

Therefore root 3 - root 2 is a irrational Number.

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