1.

Prove that 3 minus 2 root 5 is irrational number

Answer»

Heya!

Here is yr answer......


=> 3-2√5


LET US assume 3-2√5 is rational

=> 3-2√5 = a/b (a, b are any INTEGERS)

=> 2√5 = 3-a/b

=> 2√5 = 3b-a/b

=> √5 = 3b-a/2b

For any two integers RHS (3b-a/2b) is rational

but, LHS (√5) is irrational!

A rational and irrational are never EQUAL.

So, our ASSUMPTION is false

Hence, 3-2√5 is irrational


Hope it helps....

:)


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