Question

prove that root 3-root5 is an irrational number ​

Answer 1

Step-by-step explanation:

Let us assume 3+√5 is rational number. Then exists positive co-prime integers a and b such that.

3+√5=a/b

3+a/b=√5

now,

3b+a/b=√5

Therefore, √5 is irrational number

so that our assumption is wrong.

Answer 2

Answer:

Let assume that √3-√5 is a rational number, that is written in form of p/q, where p and q are integers and q ≠ 0

$\sqrt{3} - \sqrt{5} = \frac{p}{q} \\ \\ \sqrt{3}= \frac{p}{q} - \sqrt{5}$

we know √3 is irrational number, so p/q - √5 should also be irrational

there is an error in our assumption that's why

√3 - √5 must be an irrational number

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