Question

Please help me to proof this guys..

Answer 1

\[\sqrt{N + 1}-\sqrt{N}=1/ (\sqrt{N+1}+\sqrt{N})\]

Use this to explain why \[\sqrt{101}\] is close to, but slightly less than, 10.05

Answer 2

substitute
N = 100 for the equation given...

Answer 3

u will get..
\[\sqrt{100 +1} - \sqrt{100} = \frac{ 1 }{ \sqrt{100 +1} + \sqrt{100}}\]

Answer 4

hint :
times by conyugate of √(N+1) - √N, then simplify

Answer 5

since...
sqrt(100 ) = 10
u can simplify this in to
\[\sqrt{101} - 10 = \frac{ 1 }{ \sqrt{101}+ 10 }\]

Answer 6

now...
\[\sqrt{101} = \frac{ 1 }{ \sqrt{101} + 10 } + 10\]

Answer 7

yups but at the end I got
\[\sqrt{101} = \sqrt{101}\]
??

Answer 8

1/10 = 0.1
so..
1/ ( sqrt[101] + 10 ) should be even smaller than that...
because the the value of an fraction decreases when the denominator increase

so
1/ ( sqrt[101] + 10 ) is lesser than 0.1

which means the sqrt(101) is less than 10.01

furthermore
sqrt(100) = 10
therefore
sqrt(101) should equal to a value which is little bit higher than 10

if
sqrt(101) was equal to 10 then
1/ ( sqrt[101] + 10 ) will become 1/20 which is 0.5 and therefore the value of sqrt(101) will become 10.5

but
sqrt(101) is little bit higher than 10
therefore the value of
1/ ( sqrt[101] + 10 ) will be a little bit lower than 0.5
which mean
sqrt(101) is close to 10.05 but it's a little bit less than that

Answer 9

got it :) ?

Answer 10

Oh my God you are awesome! now I understand why.. Thanks!!

Answer 11

u r welcome!