pls help!

[frosty comet]

anything appreciated

[patent finch]

Im assuming this is non-calculator

My advice would be to check for a pattern

[somber trail]

Rationalise the denominator(for each fraction) you will spot a pattern

[frosty comet]

yeah i got a but im not sure what the dot dot dot means

[near violet]

add em all up, up to that point

[frosty comet]

i got 6-3√3 but not sure what to do then bc it's asking for a number and there's no option for roots

[cursive oracle]

Make sure you’re following pattern

The next term to add would be

$\frac{1}{\sqrt{3} + \sqrt{4}}$

[stuck wing]

clarence

[cursive oracle]

And then

$\frac{1}{\sqrt{4}+ \sqrt{5}}$

[stuck wing]

clarence

[frosty comet]

what so do i just add every term together up to 48 49

[cursive oracle]

Yes

There is a trick tho

[stoic folio]

||Rationalise the denominators||

[frosty comet]

yh i did

[stoic folio]

What did u get then

[frosty comet]

i got 1 once i got to 1/√3+√4

or 2-√3 which is what I got rationalised

why is this so difficult for me to understand omgg

[dusky geyser]

for part a)

after rationalising each fraction what did you get

[frosty comet]

-1+√2, √3-√2, 2-√3

[dusky geyser]

so im gonna

keep 2 written as root(4)

so you have -sqrt(1) + sqrt(2) , - sqrt(2) + sqrt(3), -sqrt(3) + sqrt(4)

right?

thats the same as what you got just rewritten

[frosty comet]

yea

[dusky geyser]

and you noticed that

loads of this cancels right

importantly each term cancels something from the one before it right

the first and second cancel the sqrt(2)

[frosty comet]

yeah

[dusky geyser]

2nd and 3rd cancel the root(3)

ok so if you went for an extra term

if you added on 1/(sqrt(4) + sqrt(5))

what would you expect that to do

or maybe try it out

[frosty comet]

-2+√5

if u rationalise

[dusky geyser]

ok and does that cancel with anything

[frosty comet]

i dont think so

wait

yes

bc √4

is 2

[dusky geyser]

exactly it cancels the root(4) from the term before

how about the next term if we added on 1/(sqrt(5) + sqrt(6))

would that cancel anything?

what would you expect

[frosty comet]

yeah the √5

[dusky geyser]

awesome so

what would you be left with then

if you added them all up until 1/(sqrt(5) + sqrt(6))

[frosty comet]

wait lemme add them

[dusky geyser]

cuz a lot cancels

[frosty comet]

-1+√6 unless ive got confused

[dusky geyser]

perfect so

only your biggest and smallest are involved right

everything inbetween cancelled

[frosty comet]

yeah

[dusky geyser]

ok so

the question for part b says

well what if you add them all up until 1/(sqrt(48) + sqrt(49)

so based on what youve just seen

[frosty comet]

ok but if you add til √6 how do u get to √49

[dusky geyser]

what will cancel? what will be left over

[frosty comet]

biggest and smallest

[dusky geyser]

exactly

the sqrt(6) will be cancelled by the next term

sqrt(7) will cancel in the term after that

sqrt(8) cancels after that

etc etc

right?

[frosty comet]

yea

is it 6

[dusky geyser]

yep

why

[frosty comet]

because just -√1 and √49 are left

[dusky geyser]

perfect exactly

everything else cancels

[frosty comet]

thankyou so much for explaining

[dusky geyser]

no worries

[frosty comet]

im gonna ss the method rq so i can use it when the question comes up again

[dusky geyser]

yep cool

just try spot patterns

[vocal shadow]

i got ||-4root3+7|| for b, is this correct?

ok defo wrong

[stoic folio]

||Its just 6 cuz all the terms cancel out to 7-1||

[vocal shadow]

can u write and show me how just for visual reference

[chilly viper]

b) Rationalise the denominators.
All numerators are one
we get so we can ignore them and look at the denominators and flip the signs
We get root 2 - 1 (root 1 is just 1) root 3 - root 2, root 49 - root 48
All values cancel out except root 49 and 1
Root 49 = 7
Root 1 = 1
7 - 1 = 6
Done

^I've also attempted this similar question on sparx and the answer was correct

[stoic folio]

(√2-√1) + (√3-√2) + ... + (√49-√48)

= -√1 + (√2-√2) + (√3-√3) + ... + (√48-√48) + √49

= -√1 + √49 = -1 + 7 = 6