Question

If 'a' and 'b' are both positive rational numbers, then
(√a-√b)(√a+√b)
a) neither rational nor rational number
b)a rational number
c) an irrational number
d) none of these​

Answer 1

Answer:

rational number

Step-by-step explanation:

as (√a-√b)(√a+√b)=a-b

and a and b both are rational

Answer 2

answer : option (b) a rational number.

then we have to check (√a - √b)(√a + √b) is rational or not .

we know from algebraic identities,

(x - y)(x + y) = x² - y²

so, (√a - √b)(√a + √b) = (√a)² - (√b)²

= a - b

it is given that a and b are two positive rational numbers.

and we know sum and difference of two rational numbers will give a rational number.

i.e., rational ± rational = rational

hence, a - b is a rational number.

so, (√a - √b)(√a + √b) is a rational number.

hence option (b) is correct choice.