Question

Prove that 3 + 2√5 is irrational.​

Answer 1

Answer:

To prove: 3 + 2√5 is an irrational number. Proof: ... This shows (a-3b)/2b is a rational number. But we know that √5 is an irrational number.

Given: 3 + 2√5

To prove: 3 + 2√5 is an irrational number.

Proof:

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

So, it can be written in the form a/b

3 + 2√5 = a/b

Here a and b are coprime numbers and b ≠ 0

Solving 3 + 2√5 = a/b we get,

=>2√5 = a/b – 3

=>2√5 = (a-3b)/b

=>√5 = (a-3b)/2b

This shows (a-3b)/2b is a rational number. But we know that √5 is an irrational number.

So, it contradicts our assumption. Our assumption of 3 + 2√5 is a rational number is incorrect.

3 + 2√5 is an irrational number

Hence proved

Step-by-step explanation:

hope it helps you!!!!!

Answer 2

Answer:

7.4721

Step-by-step explanation:

√5=2.23606

2.23606×2 =4.4721

4.4721+ 3 =7.4721