Question

Give an example each of two irrational numbers, whose
(i) difference is a rational number
(v) product is a rational number
(ii) difference is an irrational number
(vi) product is an irrational number
(iii) sum is a rational number
(vii) quotient is a rational number
(iv) sum is an irrational number
(viii) quotient is an irrational number

Answer 1

Step-by-step explanation:

(i) difference is a rational number

$\sqrt{3} - \sqrt{3} = 0$

(v) product is a rational number

$\sqrt{3} \times \sqrt{3} = 3$

(ii) difference is an irrational number

$3 \sqrt{3} - \sqrt{3} = 2 \sqrt{3}$

(vi) product is an irrational number

$\sqrt{2} \times \sqrt{3} = \sqrt{6}$

(iii) sum is a rational number

$\sqrt{3} + ( - \sqrt{3} ) = 0$

(vii) quotient is a rational number

$\frac{ \sqrt{3} }{ \sqrt{3} } = 1$

(iv) sum is an irrational number

$\sqrt{3} + 2 \sqrt{3} = 3 \sqrt{3}$

(viii) quotient is an irrational number

$\frac{2 \sqrt{3} }{2 \sqrt{2} } = \frac{ \sqrt{3} }{ \sqrt{2} }$