Question

Prove that 2 + root 5 is an irrational number.

Answer 1

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✏Prove that 2 + √5 is an irrational number .

$\large\red{\underline{{\boxed{\textbf{Brainliest\:Answer}}}}}$

☞Let $2+\sqrt{5}$ is a rational number.

Therefore, we can find two integers a,b = (b is not equal to 0) such that

$2+\sqrt{5}= \frac{a}{b}$

$\sqrt{2} = \frac{a}{b} -6$

Since a and b are integers $\frac{a}{b} -6$ also rational and hence $\sqrt{2}$ should be rational .

➡This contradicts the fact that $\sqrt{2}$ is irrational. Therefore our assupmtion is false and hence 2 +√5 is irrational.

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Answer 2

Answer:

See to my attachment.

Hope it will help you.