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Meghna deshnur

Aug 2, 2013

Give exmple of two irrational numbers whose sum is rational

Give exmple of two irrational numbers whose-

i) Sum is rational

ii) Product is rational

iii) Quotient is rational

Answers(5)

Answer

Kishore Kumar

1) (2 + √3) + (2 − √3) = 4
2) (2 + √3) × (2 − √3) = 22 − (√3)2= 4 − 3 = 1
3)  (√5/√5) = 1

Parthasaradhi M

Member since Apr 1, 2017

\\Solution:\\ Consider\ the\ two\ irrational\ numbers\ \ 3+\sqrt2\ \ and\ \ 3-\sqrt2\\\\ i)\ Sum\ of\ irrational\ numbers=(3+\sqrt2)+(3-\sqrt2)=6\ (6\ is\ rational)\\\\ ii)\ Product= ab= (3+\sqrt2)(3-\sqrt2)=3^2+\sqrt2^2=9+2=11\ (11\ is\ rational)\\\\ iii)\\ Consider\ the\ two\ irrational\ numbers\ \ \sqrt{18}\ and\ \sqrt2\\\\ Quotient=\frac{\sqrt{18}}{\sqrt2}=\frac{\sqrt{9\times2}}{\sqrt2}=\frac{\sqrt{9}\times \sqrt2}{\sqrt2}=\sqrt9=3\ \ (3\ is\ rational)

Agam Gupta

1) (2 + √3) + (2 − √3) = 4
2) (2 + √3) × (2 − √3) = 22 − (√3)2= 4 − 3 = 1
3) �(√5/√5) = 1

Syeda

Answer.

 (2 + √3) + (2 − √3) = 4
 (2 + √3) × (2 − √3) = 22 − (√3)2= 4 − 3 = 1
 (√5/√5) = 1

Ashok K Singh

Two irrational numbers whose
 (i) sum is rational are
10 + 2√5 and 5 - 2√5 
Checking:
Sum of these two irrational numbers = 
10 + 2√5 and 5 - 2√5 = 15 (a rational number)

(ii) 
 product is rational are
10 + 2√5 and 10 - 2√5 
Checking:
Product of these two irrational numbers
                    = (10 + 2√5) (10 - 2√5)
                    = (10)2 -  (2√5)2 
                    = 100 - 20 = 80 (a rational number)
(iii) 
 quotient is rational are
                 10√5 and 5√5 
Checking:
Quotient of these two irrational numbers = 
                 (10√5)/(5√5) = 2 (a rational number)
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