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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

Agam Gupta

Member since Sep 21, 2013

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

Member since Jan 25, 2017

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

Member since

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)

Kishore Kumar

Member since

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
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