Question

Show that 5 root 3 minus 2root 7 is an irrational

Answer 1

Answer:

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

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Step-by-step explanation:

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Answer 2

Step-by-step explanation:

Let as assume on contrary that 

√3 + √5 

is a rational number. 

Then there exists co - prime integers p and q such that  



⇒  √3 

is a rational number . 



But this contradicts the fact that 

√3  

is  irrational.

So, our assumption is wrong.

Hence,

√3  + √5 

is  irrational.