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root 2+root 3 is it a rational number justify square root of 2 plus square root of 3 space i s space i t space a space r a t i o n a l space n u m b e r ? j u s t i f y
Asked by flowtoofar | 11 Jul, 2019, 06:45: AM
answered-by-expert Expert Answer
 
begin mathsize 16px style Suppose space space square root of 2 plus square root of 3 space equals space straight x space is space straight a space rational space number. open parentheses square root of 2 plus square root of 3 space close parentheses squared space equals space straight x squared rightwards double arrow space 5 space plus space 2 square root of 6 equals space straight x squared rightwards double arrow square root of 6 space equals space fraction numerator straight x squared space minus space 5 over denominator 2 end fraction Since comma space it space is space assumed space that space square root of 2 plus square root of 3 space equals space straight x space is space straight a space rational space number. rightwards double arrow straight x squared space is space also space straight a space rational space number. rightwards double arrow fraction numerator straight x squared space minus space 5 over denominator 2 end fraction is space also space straight a space rational space number rightwards double arrow square root of 6 space is space straight a space rational space number But space we space know space that space square root of 6 space is space an space irrational space number So comma space we space arrive space at space straight a space contradiction. rightwards double arrow square root of 2 plus square root of 3 space is space an space irrational space number. end style
Answered by Yasmeen Khan | 11 Jul, 2019, 10:48: AM

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