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2014-08-10T19:45:58+05:30

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x² = 49 / 20

x = 7 / 2√5  = 0.7 √5
√5 cannot be expressed as a rational number.  so x is an irrational number.

another way.
y² - 5 = 0            Rational roots if any could be : +- factors of 5 / +-1
                                                 =  +- 5
Since y is not equal to +- 5, It implies that no rational roots exist for y² - 5 =0
So y is irrational.    So √5 is irrational.

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2014-08-10T20:44:12+05:30