Question

prove that 5 - 2√3 is an irrational number ​

Answer 1

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Answer 2

Step-by-step explanation:

Let us assume to the contrary that 5-2√3 is rational.

=>5-2√3=p/q

=>-2√3=p/q-5

=>-2√3=p-5q/q

=>√3=p-5q/-2q

Here, p-5q/ -2q is a rational number. This says that √3 is rational. But this contradicts the fact that √3 is irrational. This contradiction arises because of our wrong assumption that 5-2√3 is rational.

Therefore, 5-2√3 is irrational.