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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

#### question_answer Answers(5)

Answer

Kishore Kumar

1) (2 + âˆš3) + (2 âˆ’ âˆš3) = 4 2) (2 + âˆš3) Ã— (2 âˆ’ âˆš3) = 22 âˆ’ (âˆš3)2= 4 âˆ’ 3 = 1 3)  (âˆš5/âˆš5) = 1

Parthasaradhi M

Member since Apr 1, 2017

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

Agam Gupta

1) (2 + âˆš3) + (2 âˆ’ âˆš3) = 4 2) (2 + âˆš3) Ã— (2 âˆ’ âˆš3) = 22 âˆ’ (âˆš3)2= 4 âˆ’ 3 = 1 3) ï¿½(âˆš5/âˆš5) = 1

Syeda

Answer.  (2 + âˆš3) + (2 âˆ’ âˆš3) = 4  (2 + âˆš3) Ã— (2 âˆ’ âˆš3) = 22 âˆ’ (âˆš3)2= 4 âˆ’ 3 = 1  (âˆš5/âˆš5) = 1

Ashok K Singh

Two irrational numbers whose  (i) sum is rational are 10 + 2âˆš5 and 5 - 2âˆš5  Checking: Sum of these two irrational numbers = 10 + 2âˆš5 and 5 - 2âˆš5 = 15 (a rational number) (ii)  product is rational are 10 + 2âˆš5 and 10 - 2âˆš5  Checking: Product of these two irrational numbers                     = (10 + 2âˆš5) (10 - 2âˆš5)                     = (10)2 -  (2âˆš5)2                      = 100 - 20 = 80 (a rational number) (iii)  quotient is rational are                  10âˆš5 and 5âˆš5  Checking: Quotient of these two irrational numbers =                   (10âˆš5)/(5âˆš5) = 2 (a rational number)
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