Question

prove that 3plus 2root5 is irrational

Answer 1

Answer:

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

Then, there exist co - primes a and b (b not equal to 0 )such that

3+2√5 = a/b

2√5 = a/ b - 3

2√5 = a - 3b / b

√5 = a - 3b/2b

since a and b are integers , so that a- 3b/ 2b is rational.

Thus, √5 is also rational.

But, this contradicts the fact that √5 is irrational. So , our assumption is incorrect.

Hence, 3+2√5 is irrational .

HOPE! it's helps u.....xd....xd.

Answer 2

Answer:

Step-by-step explanation:let assume 3+2√5 = rational

2√5 = rational - 3 ( rational - 3 = rational)

√5 = rational/2 (rational/2 =rational)

So

√5 = rational

But we know that √5 is irrational

Irrational not equal to rational

So our assumption is wrong

3+2√5 is irrational