Question

18. Prove that 3 - 2/5 is irrational.​

Answer 1

Answer:

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Answer 2

Let us assume to the contrary that  $3-2\sqrt{5}$ is rational

Hence it can be expressed in the form of  $\frac{p}{q}$ where p and q are integers and q≠0

Hence

$3-2\sqrt5 = \frac{p}{q}$

$-2\sqrt5 = \frac{p-3q}{3q}$

$\sqrt5 = \frac{3q-p}{6q}$

p,q,3 and 6 are all rational numbers

Hence $\frac{3q-p}{6q}$ is rational

But $\sqrt5$ is irrational

This is a contradiction

This has arisen due to our wrong assumption that  $3-2\sqrt{5}$ is rational

Hence our assumption is wrong

Hence  $3-2\sqrt{5}$ is irrational

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