Question

Hø|á !!

Prove that 1/3-2√5 is an irrational number.

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Answer 1

First of all, can you say, is √5 an irrational number or not?

You can surely say and can also prove that.

So, since you already knew that √5 is an irrational number, i am not proving it once again. But you have to prove that √5 is an irrational number at the very beginning of your solution.

______________________________

Let, 1/3 - 2√5 be a rational number.

So, we can proceed as under :

1/3 - 2√5 = r

Or, -2√5 = r - 1/3

Or, √5 = (r - 1/3)/(-2)

Now, √5 is here equal to "(r - 1/3)/(-2)". So, now we know that, √5 is irrational. Since both of them are equal, if √5 is irrational, then the Right Hand Side term will also be an irrational number.

Hence, finally, what do you conclude?

You can be able to conclude that our assumption is wrong.

So, we can say 1/3 - 2√5 is an irrational number. Hence, its proved.

Answer 2

hi friend here is your answer

# 1 by 3 minus 2 root 5 is irrational. ... IS ALSO A IRRATIONAL NUMBER. so 1/3 - 2√5is irrational.

1
------ -2 √5
3

hope it helps u friend plz mark as brainlist