Question

Could u please answer this question?

Answer 1

Explanation:

1/(1 + sqrt(2))

remember the fact that

(a + b)(a - b) = a² - b²

so, I can multiply the fraction by

(1 - sqrt(2))/(1 - sqrt(2))

and I get

(1 - sqrt(2))/(1 - 2) = -(1 - sqrt(2)) = sqrt(2) - 1

the same for

1/(sqrt(2) + sqrt(3))

we multiply by

(sqrt(2) - sqrt(3))/(sqrt(2) - sqrt(3))

and get

(sqrt(2) - sqrt(3))/(2 - 3) =

= -(sqrt(2) - sqrt(3)) = sqrt(3) - sqrt(2)

and we do this for every fraction.

we get

sqrt(2) - 1 + sqrt(3) - sqrt(2) + sqrt(4) - sqrt(3) + sqrt(5) - sqrt(4) + sqrt(6) - sqrt(5) + sqrt(7) - sqrt(6) + sqrt(8) - sqrt(7) + sqrt(9) - sqrt(8) =

= sqrt(9) - 1 =

= 3 - 1 = 2

Answer 2

`√(8 + 1) - 1`