Question

show that 2+root 3 is an irrational number, given that root 3 is irrational ​

Answer 1

Answer:

value of root3 is 1.73205080....

so if we add value of root3 to 2, it becomes

2+ 1.73205080...

=3.173205080

this is a irrational no.

proved

Step-by-step explanation:

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Answer 2

Answer:

let 2+ root 3 is a rational no.

a/b = 2+ root 3 , where a and b are co - primes and b is not equal to zero..

a/b - 2 = root 3

now, lcm a/b - 2 we get,

a - 2b / b = root 3

we get a - 2b/b is a rational no. so, root 3 is also a rational no.

but this contradicts the fact that root 3 is a irrational no.

hence 2 + root 3 is a irrational no............

Step-by-step explanation:

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