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Given that Root 5 is irrational ,prove that 2root 5-3 is an irrational no. |
| Answer» Let us assume on the contrary that 2√5-3 is rational. Then,there exist co-prime integer a and b such that 2√5-3=a/b2√5=a/b+3√5=1/2(a/b-3) ( that is a,b are integer,therefore 1/2 (a/b -3) is a rational no.)We know that,√5 is an irrational no. (given)This is contradicts the fact that √5 is irrational.So, our assumption is incorrect.Hence ,2√5 -3 us an irrational number.?? | |