Question

pls answer this guy's tomorrow is my test with steps please

Answer 1

i) 1/(√100 + √99) = (√100 - √99)/{(√100 + √99)*(√100 - √99)
= (√100 - √99)/(100 - 99) [By algebra identity, (a + b)*(a - b) = a² - b²]
= √100 - √99

ii) Similarly rationalizing every term,
2nd is: √99 - √98; 3rd is: √98 - √97; 4th is: √97 - √96 and so on.......
Last term is: √2 - √1

iii) Thus the sum k = √100 - √99 + √98 - √97 + √97 - √96 + ....................... + √2 - √1
Simplifying, all middle terms cancels out, but for the two extremes.
==> k = √100 - √1 = 10 - 1 = 9

So k² = 9² = 81

Note: This is my own original solution. Kindly aware that I have not copied it from Net.