Math, asked by rsriram, 1 year ago

prove that root 2 + root 7 is not rational number

Answers

Answered by purvisri02
126
√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
Answered by piyushgoel288
41

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