Question

pt 3+2√5 is irrational​

Answer 1

HELLO MATE HERE IS YOUR ANSWER

RTP 3+2root5 is irrational

Step by step explanation

We need to prove that3+2√5 is irrational.

Let take that 3 + 2√5 is a rational number.

So we can write this number as

3 + 2√5 = a/b

Here a and b are two co prime number and b is not equal to 0

Subtract 3 both sides we get

2√5 = a/b - 3

2√5 = (a-3b)/b

Now divide by 2 we get

√5 = (a-3b)/2b

Here a and b are integer so (a-3b)/2b is a rational number so √5 should be a rational number But √5 is a irrational number so it contradict the fact

Hence result is 3 + 2√5 is a irrational number

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Answer 2

Heya!

Here is ur answer....

Let us assume 3+√2 is rational..

Now,

3+2√5 = a/b [ a,b € Z]

2√5 = a/b-3

2√5 = a-3b/b

√5 = a-3b/2b

Here,

For any two integers (a,b) RHS(a-3b/2b) is rationa.

But, LHS is irrational (√5)

A rational and Irrational are never equal

Therefore, our assumption is false!

Hence, 3+2√5 is irrational

Hope it helps u..