Question

prove that 3+2√5 is irrational​

Answer 1

Answer:

Hope answer will help u

Answer 2

Question

prove that 3+2√5 is irrational

Answer

we have to prove 3 + 2 root 5 is irrational

Let us assume the opposite , that 3+2√5is rational .

Hence, 3+2√5 can be written in the form of p/q where p and q are integers and q is not equal to 0 .

Now,

3+2√5=a/b

=> 2√5=a/b - 3

=> 2√5= a-3b/b

=> √5 = 1/2×a-3b/a

=> √5 = a-3b/2b

Here √5 is irrational number .

here a-3b/2b is rational .

Now,

Here, a-3b/2b is a rational no. and √5 is irrational .

So, rational is not equal to irrational

This contradiction says that our assumption is wrong .

Hence proved , 3+2√5 is a irrational number .