9TH CLASS REAL NUMBER | PRACTICE SET2.2 | MAHARASHTRA BOARD | 3 NUMBERS BETWEEN 2 RATIONAL NUMBERS

(1) Addition or subtraction of a rational number with irrational number is an irrational number.
(2) Multiplication or division of non zero rational number with irrational number is also an
irrational number.
(3) Addition, subtraction, multiplication and division of two irrational numbers can be either a rational or irrational number.
We know that, if a = b then b2
= a.
Hence if 5 = x then x2
= 5.
Similarly we know that square of any real number is always non-negative. It means that
square of any real number is never negative. But ( -5 )2
= -5 \ -5 is not a real number.
Hence square root of a negative real number is not a real number

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