Question

Prove that 5-2root3is irrational number

Answer 1

Hii friend!!

assume that 5-2 root 3 is rational

5-2 root 3 = a/b , where a and b are integers . 

-2 root 3 = a/b - 5

2 root 3 = 5 - ab 

2 root 3 = 5b/b - a/b

root 3 = 5b - a / 2b

we know that a, b , 2 and 5 are integers and they are also rational 

therefore root 3 will be rational 

but we know that root 3 is irrational

there is a contradiction

so, 5 - 2 root 3 is an irrational number

hope u found it useful ^_^ 

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Answer 2

hola!!!! mate

here is your answer

let assume that 5 + 2√3 = r , where "r" is rational

2√3 = r - 5

√3 = r-5/2

Here , we can see that the RHS is purely rational , whereas LHS is irrational.

This leads to a contradiction . Hence, our assumption was wrong.

Therefore, 

5 + 2√3 is irrational. 

hope it helps you

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