Question

Give an example of 2 irrational numbers , whose

1.difference is a rational number
2.difference is an irrational number
3.sum is a rational number
4.sum is a irrational number
5.product is a rational number
6.product is a irrational number
7.quotient is a rational number
8.quotient is a rational number


PLEASE ANSWER ASAP

Answer 1

1. If a = 12 + √3 and b = 3 + √3

The difference,

a - b = 12 + √3 - 3 - √3

= 9

It is a rational number

2. If a = √46 and b = √86

The difference,

a - b = √46 - √86

It is a irrational number

3. If a = 3 + √3 and b = 4 - √3

The sum,

a + b = 3 + √3 + 4 - √3 = 7

It is a rational number

4. If a = 46 - √3 and b = 46 + √5

The sum,

a + b = 92 + √5 - √3

It is a irrational number

5. If a = 7 + √5 and b = 7 - √5

The product,

ab = (7 + √5)(7 - √5) = 49 - 5 = 44

It is a rational number

6. If a = 2√6 and b = 7√8

The product,

ab = (2√6)(7√8)

= 14√48

It is a irrational number

7. If a = 5√7 and b = 4√7

The quotient,

$\frac{a}{b} = \frac{ 5\sqrt{7} }{4 \sqrt{7} } = \frac{5}{4}$

It is a rational number

8. If a = √8 and b = √24

The quotient,

$\frac{a}{b} = \frac{ \sqrt{8} }{ \sqrt{24} } = \frac{1}{ \sqrt{3} }$