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Prove that √6+√2 is irrational

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Prove that √6+√2 is irrational

    • Posted by Krishika Pandhi 6 years, 5 months ago

    CBSE > Class 10 > Mathematics
    • 1 answers

    Sia ? 6 years, 5 months ago

    Let take that 6 + √2 is a rational number.
    So we can write this number as
    6 + √2 = a/b
    Here a and b are two co-prime number and b is not equal to 0
    Subtract 6 both side we get
    √2 = a/b – 6
    √2 = (a-6b)/b
    Here a and b are an integer so (a-6b)/b is a rational number so √2 should be a rational number But √2 is an irrational number so it is contradicting
    Hence result is 6 + √2 is a irrational number

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