Prove that V7 + V2 is an irrational number.

1.	Prove that V7 + V2 is an irrational number.
Answer» √2 +√7 = a/b (where a and b are co-prime)√7 = a/b -√2Squaring both sidesa²/b² - 2√2a/b + 2 = 7a²/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. V7+V2 x V7-V2/V7-V2= (V7)^2-(V2)^2/V7-V2=7-2/V7-V2=5/V7-V2

Answer»

√2 +√7 = a/b (where a and b are co-prime)√7 = a/b -√2Squaring both sidesa²/b² - 2√2a/b + 2 = 7a²/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.

V7+V2 x V7-V2/V7-V2= (V7)^2-(V2)^2/V7-V2=7-2/V7-V2=5/V7-V2

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