Question

30. Prove that 5-√3 is irrational, given that V3 is irrational.​

Answer 1

5-√3 is irrational

Step-by-step explanation:

Let us assume that 5 - √3 is a rational

We can find co prime a & b ( b≠ 0 )such that 5 - √3 = a/b

Therefore 5 - a/b = √3

So we get 5b -a/b = √3

Since a & b are integers, we get 5b -a/b is rational, and

so √3 is rational. But √3 is an irrational number

Let us assume that 5 - √3 is a rational We can find co prime a & b ( b≠ 0 )such that

∴ 5 - √3 = √3 = a/b

Therefore 5 - a/b = √3

So we get 5b -a/b = √3

Since a & b are integers, we get 5b -a/b is rational, and so √3 is rational.But √3 is an irrational number Which contradicts our statement

∴ 5 - √3 is irrational

Answer 2

Answer:

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