Question

Prove that root 3 +2 root 5 is irrational

Answer 1

Answer:

Step-by-step explanation:

We need to prove that√3+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

Answer 2

a = 3+2root 5 here a is rational and co-prime number

a -3=2root5

it contradicts as 2 root 5 is irrational so 3+2root5is irrational