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Given : 7 − √5
LET US ASSUME THAT 7 − √5 IS RATIONAL NUMBER
∴ 7 − √5 = a/b (a,b ∈ z , where b ≠ 0)
−√5 = a/b − 7
√5 = 7 − a/b
IF a,b ARE INTEGERS THEN 7 − a/b IS RATIONAL NUMBER.
SO √5 IS ALSO A RATIONAL NUMBER.
BUT THIS CONTRADICTS THE FACT THAT √2 IS IRRATIONAL.
∴ WE CONCLUDE THAT 7 − √5 IS IRRATIONAL NUMBER.
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harish611:
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