Question

prove that 3+2root5 is an irrational
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Answer 1

Answer:

$3 + 2 \sqrt{5} \\ 5 \sqrt{5} \\ 5$

it is irrational number ok

Step-by-step explanation:

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Answer 2

Answer:

According to you, we have to prove $3+2\sqrt{5}$ as irrational.

$So, let \\3+2\sqrt{5}$

be rational. Therefore it can be written in $\frac{p}{q}$ form.

$so,\\3+2\sqrt{5}=\frac{p}{q}\\or, \sqrt{5}= \frac{(\frac{p}{q}-3)}{2}\\or, \sqrt{5}= \frac{p-3q}{2q}$  but p, q, 2, 3 are all integers ∴  the expression is rational, but it              contradicts the fact that $\sqrt{5}$ is irrational.

∴$3+2\sqrt{5}$ is irrational.

Step-by-step explanation: