Question

prove that 3+2√5 is a irrational​

Answer 1

Answer:

look below

Step-by-step explanation:

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

hope you are helped

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give brainliest if it is correct

Answer 2

Step-by-step explanation:

let us think that 3+2√5 is rational and every rational no. are in form of p/q where q nor =0 there fore 3+2√5=p/q

3=p/q =√5

3p/q =√5

now 3divides both p and q there fore it is rational no. but it contradicts that 2√5is irrational and our assumption is wrong that 3+2√5is rational

there fore 3+2√5is irrational

Hence provef