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Aug 2, 2013

Give exmple of two irrational numbers whose-

i) Sum is rational

ii) Product is rational

iii) Quotient is rational

i) Sum is rational

ii) Product is rational

iii) Quotient is rational

Kishore Kumar

1) (2 + âˆš3) + (2 âˆ’ âˆš3) = 4

2) (2 + âˆš3) Ã— (2 âˆ’ âˆš3) = 2^{2} âˆ’ (âˆš3)^{2}= 4 âˆ’ 3 = 1

3) (âˆš5/âˆš5) = 1

2) (2 + âˆš3) Ã— (2 âˆ’ âˆš3) = 2

3) (âˆš5/âˆš5) = 1

Parthasaradhi M

Member since Apr 1, 2017

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

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

(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)

(i) sum is rational are

Checking:

Sum of these two irrational numbers =

(ii)

Checking:

Product of these two irrational numbers

= (10 + 2âˆš5) (10 - 2âˆš5)

= (10)

= 100 - 20 = 80 (a rational number)

(iii)

Checking:

Quotient of these two irrational numbers =

(10âˆš5)/(5âˆš5) = 2 (a rational number)