Question

1 upon 1+ root 2 + 1 upon root 2 + root 3 + 1 upon root 3 + root 4 + 1 upon root 4 + root 5 + 1 upon root 5 + root 6.... +1 upon root 8 + root 9=2 rationalising the denominator

Answer 1

1/(1 + √2) + 1/(√2 + √3) + 1/(√3 + √4)..
.....1/(√8 + √9) = 1

now, 1/(1 + √2) = (1 - √2)/(1 + √2)(1 - √2)

(1 - √2)/(1 - 2) = (√2 - 1)

1/(√2 - √3) = (√2 + √3)/(√2 - √3)(√2 + √3)

(√2 + √3)/(2 - 3) = (√3 - √2)
and so, on.....

√2 - 1 + √3 - √2 + √4 - √3 +.......√9 - √8

= 3

Answer 2

Answer:

Step-by-step explanation:

1/(1 + √2) + 1/(√2 + √3) + 1/(√3 + √4)..

.....1/(√8 + √9)

now, 1/(1 + √2) = (1 - √2)/[(1 + √2)(1 - √2)]

(1 - √2)/(1 - 2) = (√2 - 1)

1/(√2 + √3) = (√2 -√3)/[(√2 + √3)(√2 -√3)]

(√2 - √3)/(2 - 3) = (√3 - √2)

and so, on.....

After rationalising each term u get

√2-1+√3-√2+√4-√3+√5-√4+√6-√5+

√7-√6+√8-√7+√9-√8

= -1 +√9

= -1 + 3

=2.