Question

prove that root3+root5 is irrational

Answer 1

Answer:

Step-by-step explanation:

Answer 2

Hola mate..

Here's ur answer..

Answer :

Let us assume the contrary,

$i.e \: \sqrt{3 } \: + \sqrt{5}$

Is irrational thus their can be two integers a and b (b ≠0) and a and b are co-prime numbers, so that

$= \sqrt{3 } \: + \sqrt{5} = \frac{a}{b}$

$b \sqrt{3} + \sqrt{5 } = a \: \\ squaring \: on \: both \: sides \: \\ {b}^{2} \: ( \sqrt{3} \: + \ \sqrt{5} ) \: {a}^{2}(canceling \: the \: roots) \\ = {b}^{2} (3 + 5) = {a}^{2} \\ 8 {b}^{2} = {a}^{2}$

This means that 8 divides a^2 and hence 8 divides "a" also.

This means contradicts our earlier assumption that a and b are co-prime, because 8 is at least one common factor of a and b.

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