Question

5. Prove that 3 + 2√5 is irrational, using the fact that √5 is irrational.

Standard:- 10

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Answer 1

Your answer is --

Let, us assume that 3+2√5 is rational .

So, 3+2√5 = a/b where a and b are integer and b ≠ 0 .

=> 2√5 = a/b - 3 = (a-3b)/b

=> √5 = (a-3b)/2b

Since, (a-3b)/2b is rational because a and b are integer and b ≠ 0

Therefore , √5 is also a rational number
[ °•° √5 = (a-3b)/2b ]

But, this contradict the fact that √5 is irrational .

So, our assumption is wrong

Hence, 3+2√5 is irrational .

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