Question

Prove that {(3√5)-2} is an irrational number?????

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Answer 1

Answer:

is this long questions ..

Answer 2

Answer:

{(3√5)-2} is an irrational number.

Step-by-step explanation:

Given that the number is, {(3√5)-2}

Let us assume that the number is  {(3√5)-2} is a rational number.

Then we can write , {(3√5)-2}= a/b  , where b≠0, a≠b , and  a, b∈ R

Now,

{(3√5)-2}= a/b

$or, 3\sqrt{5} = a/b+2$

$or, \sqrt{5}=\frac{(a+2b)}{3b}$----(i)

From the above equation (i) we can say that √5 is a rational number.

But, we know that √5 is an irrational number.

This shows that our assumption is contradict .That means  {(3√5)-2} is

not a rational number . that is,  {(3√5)-2} is an irrational number.

Hence the proof.