Question

rationalize: 3 upon 2-√5​

Answer 1

Answer:

≈ -12.70

Step-by-step explanation:

= 3/2-√5

= 3/2-√5 × 2+√5/2+√5

= 3(2+√5)/(2-√5)×(2+√5)

= 3(2+√5)/4-5

= (3+2√5)/-1

= -3(2+√5)

= - 6 - 3√5

≈ -12.70

Answer 2

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