Question

prove that 7- 2 root 3 is an irrational number

Answer 1

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Answer 2

Answer:

Step-by-step explanation:

Let us assume to contrary that 7-2√3

is not an irrational number....

So 7-2√3 is rational number..

So, a/b=7-2√3 (a not equal to b and a and b are coprime)

a/b-7=-2√3

(a-7b)/b=-2√3

(a-7b)/-2b=√3

We know that √3 is an irrational number, and a rational number can't be equal to an irrational number..

So, 7-2√3 is an irrational number...

Hence proved..

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