Question

Prove that 2root3 is not a rational number 10th class 1st chapter real numbers

Answer 1

To prove = 2√3 is an irrational number.

We shall prove this by the method of contradiction .

so let us assume to the contrary that 2√3 is a rational number =r

2√3=r

√3=r/2

Now we know that √3 is irrational number.

SO, r/2 has to be irrational to make the equation true .

This is a contradiction to our assumption . Thus our assumption is wrong .

Therefore,2√3 is irrational .

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Answer 2

Answer:

Assume that 2 root 3 is a rational number.

2root3 = a/b (where a and b are integers and b is not equal to 0)

root 3 = a/b-2

root3 = a- 2b/ b

here, a-2b/b is a rational number

Since sum, difference, product and quotient of two integers is an integer

Therefore, root 3 is a rational number

This is a contradiction to the fact that root 3  is a irrational and this contradiction is due to our wrong assumption that 2 root 3 is a rational number.

Therefore, 2 root 3 is an irrational number