show that 5+√7 is an irrational number
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Step-by-step explanation:
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Step-by-step explanation:
Let,
5 + √7 be a / b.
a and b are co - primes.
5 + √7 = a / b
√7 = ( a / b ) - 5
= ( a / b ) - ( 5b / b )
√7 = ( a - 5b ) / b
√7 is rational, which is contradiction to the fact that √7 is irrational. Our assumption is wrong.
Therefore,
5 + √7 is an irrational number.
Hence proved.
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