Question

prove that that no. is irrational (2-√3)​

Answer 1

let us assume that 2√3 is a rational no.

2√3=a/b(where a Nd b are co prime no.)

squaring both side

12=a^2/b^2

12b^2=a^2............k

12 is a factor of a^2

12 will be factor of a.....................1

let a=12c

squaring both side

a^2=144c^2...................ll

putting ll in k

12b^2=144c^2

b^2=12c^2

12 is a factor of b^2

12 will be factor of b..............lll

from 1&lll

12 is the factor of both a&b

so, they are not co prime no.

hence our assumption is wrong

2√3 is an irrational no.

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Answer 2

Answer:

let us assume that 2√3 is a rational no. 2√3=a/b(where a Nd b are co prime no.) ... 2√3 is an irrational no.Nov 8, 2017