Question

Let x and y be rational and irrational numbers respectively are x+y and xy irrational? Justify your answer by an example for each

Answer 1

Hello Dear!!!

Here's your answer..

Lets take example-

Let,

x=√2

y=√3

Now,

x+y

√2+√3

it is irrational

AND

xy

√2*√3

√6

it is irrational

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Answer 2

Two irrational numbers whose
 (i) sum is rational are
10 + 2√5 and 10 - 2√5 
Checking:
Sum of these two irrational numbers = 10 + 2√5 and 10 - 2√5 = 20 (a rational number)

(ii)  product is rational are
10 + 2√5 and 10 - 2√5 
(10+2root5)(10-2root5)
${10}^{2} - 2 {}^{2} \sqrt{5 ^{2} }$
$100 - 20$