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Prove that root 6 + root 7 is an irrational number

Answer»

6 + √7 is irrational NUMBER

__________ [TO PROVE]

Let us ASSUME that, 6 + √7 is a rational number

=> 6 + √7 = \dfrac{a}{b}

Here, a and b are co-prime NUMBERS.

=> √7 = \dfrac{a}{b} - 6

=> √7 = \dfrac{a\:-\:6b}{b}

Here..

\dfrac{a\:-\:6b}{b} is rational number.

So, √7 is also a rational number.

But we know that √7 is irrational number.

So, our ASSUMPTION is wrong.

6 + √7 is irrational number.

___________ [HENCE PROVED]


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