Question

give an example of each of two irrational numbers whose :- a) difference is a rational no. b) difference is an irrational no. c) sum is a rational no. d) sum is an irrational no. e) product is a rational no. f) product is an irrational no. g) quotient is a rational no. and quotient is an irrational no.

Answer 1

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i) 2 + √5 , and 3 + √5

ii) 10 + 3 , 5 - √3

iii) 3 +√2 , 3 - √2

iv) 5√3 , 3√3

v) 3 - √5 , 5 +√3

vi) 5 √8 , √2

vii) 2√3 , √3

viii) 2√10 , 2√2

Step-by-step explanation:

Answer 2

(a) two irrational nos. whose difference is rational no.

$\sqrt{2} -\sqrt{2} = 0$

(b) two irrational nos. whose difference is an irrational no.

$\sqrt{3} -\sqrt{2}=\sqrt{1}$

(c) two irrational nos. whose sum is a rational no.

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

(d) two irrational nos. whose sum is an irrational no.

$\sqrt{5} +\sqrt{3}$

(e) two irrational nos. whose product is a rational no.

$\sqrt{3} +\sqrt{2}* \sqrt{3}-\sqrt{2}$

(f) two irrational nos. whose product is an irrational no.

$\sqrt{3} *\sqrt{5}$

(g) two irrational nos. whose quotient is a rational no.

$6\sqrt{2} and 2\sqrt{2}$

(h) two irrational nos. whose quotient is an irrational no.

$\sqrt{3} and \sqrt{5}$

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