Question

proof that 4+√5 is irrational number ​

Answer 1

Answer:

hey mate

here's your answer

basically, the logic behind this is..

any irrational number added to a whole number will give you an irrational number

hope you are clear! :)

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Answer 2

Lets assume that $\sf{4 + \sqrt{5}}$ is a rational number.

$\sf{\implies 4 + \sqrt{5}=\dfrac{p}{q}}$ where p and q are integers.

$\sf{\implies \sqrt{5}=\dfrac{p}{q}-4}$

$\sf{\implies \sqrt{5}=\dfrac{p-4q}{q}}$

Since, p - 4q and q are integers .

$\sf{ \sqrt{5}}$ is a rational number which is a contradiction.

So, our assumption is wrong.

Hence, $\sf{4 + \sqrt{5}}$ is an irrational number.

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