Question

proove that √7 - √5 is irrational

Answer 1

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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

Hope it's help uh

Answer 2

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