Question

If a and b are natural number then (root a + root b) (root a - root b ) is rational .Is it true ?​

Answer 1

Answer:

True

Step-by-step explanation:

Because,

if a and b are natural number

then

(root a + root b)(root a - root b)

= (√a + √b) (√a - √b)

= (√a)² - (√b)²

[because (a+b)(a-b) = a² - b², here a = √a and b = √b]

= (√a)² - (√b)²

= a - b

Because a and b are natural number, so their difference will be a natural number and every natural number is a rational number.

Hence (root a + root b) (root a - root b) is rational.

hope it helps.