Question

prove that (2+3√3) is an irrational number. Give that √3 is an a irrational ​

Answer 1

Answer:

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Answer 2

Given

√3 is irrational number

Let 2+√3 is rational number.

then, 2+√3 = $\frac{p}{q}$

√3 = $\frac{p - \sqrt{2} q}{q}$

Since

√3 is irrational number but $\frac{p - \sqrt{2} q}{q}$ is rational it mean irrational = rational.

which contradict,

∴ our assumption is wrong and 2+√3 is irrational number.