Question

prove that √2+√7 is an irrational number​

Answer 1

LET US ASSUME THAT √2+√7AS RATIONAL.

√2 + √7 = a/b           

  (where a and b are co-prime)

√7 = a/b - √2

Squaring both sides

a²/b² - 2√2a/b + 2 = 7

a²/b² - 5 = 2√2a/b

(a² - 5b²) / 2ab  = √2

√2 is an irrational number .

This contradicts the fact that √2 is irrational . So , our assumption is wrong.

Hence , 

                  √2 + √7 is irrational