Question

prove that root 7 +2 root 3 is irrational number​

Answer 1

Step-by-step explanation:

let 7+2√3 is a rational number

and rational number is in form p/q

so , 7+2√3 = a/b

2√3 = a/b - 7

2√3 = (a - 7b)/b

√3 = (a - 7b)/2b

(a - 7b)/2b is a rational number

but √3 is a rational number

so , our assumption is wrong

7+2√3 is a rational number

Answer 2

Answer:

Step-by-step explanation:

Step-by-step explanation:

Let us assume that √3+√7 is rational.

That is , we can find coprimes a and b (b≠0) such that

Therefore,

Squaring on both sides ,we get

Rearranging the terms ,

Since, a and b are integers , is rational ,and so √3 also rational.

But this contradicts the fact that √3 is irrational.

This contradiction has arisen because of our incorrect assumption that √3+√7 is rational.

Hence, √3+√7 is irrational.