Question

Out of the following irrationals, which has sum and product both rationals? Give reason. (a) √3 + 5 and √3 - 5
(b) √3 + √5 and √3 - √5
(c) 5 + √3 and 5 - √3
(d) All of these

Answer 1

answer : option (c) 5 + √3 and 5 - √3

let's see all options one - by - one.

option (a) √3 + 5 and √3 - 5

sum = (√3 + 5) + (√3 - 5) = 2√3 ≠ rational number

so option (a) is incorrect.

option (b) √3 + √5 and √3 - √5

sum = (√3 + √5) + (√3 - √5) = 2√3 ≠ rational number

also option (b) is incorrect.

option (c) 5 - √3 and 5 + √3

sum = (5 - √3) + (5 + √3) = 10 = rational number

product = (5 - √3)(5 + √3) = 25 - 3 = 22 = rational number

here it is clear that, sum and product, both are rationals so option (c) is correct choice.

Answer 2

Answer:

option C is correct

Step-by-step explanation:

sum = (5 - √3) + (5 + √3) = 10 = rational number

product = (5 - √3)(5 + √3) = 25 - 3 = 22 = rational number

here it is clear that, sum and product, both are rationals so option (c) is correct choice.