show that 2 + root 7 is an irrational number
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be a rational number which can be expressed in the form of p/q where p and q are integers, relatively prime and q is not equal to zero. is a rational number which is not
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let 2+√7 be rational
2+√7=p
√7=p-2
we know that p is a rational number
therefore p-2 is rational and thus √7 is also rational which contradicts that √7 is irrational
therefore our assumption is wrong
2+√7 is irrational
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