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Can't understand question in C4 June 2013 (R)

I just don't get the question in C4 June 2013 (R) question 4b on binomial expansions.

I can't post it here but the mark scheme solution to the question is just bizarre.
If anyone can explain it to me it would be great.

Reply 1

HapaxOromenon3

Original post by kc006

note that cube root of 7100 = cube root of (1000 * 7.1) = 10 * cube root of 7.1
Now set 8 - 9x = 7.1 -> 9x = 0.9 -> x = 0.1.
Hence put 0.1 into your expansion from part (a) to get the approximation.

Reply 2

kc006

Original post by HapaxOromenon3

note that cube root of 7100 = cube root of (1000 * 7.1) = 10 * cube root of 7.1
Now set 8 - 9x = 7.1 -> 9x = 0.9 -> x = 0.1.
Hence put 0.1 into your expansion from part (a) to get the approximation.

wait isnt the cube root of (7100) the same as cube root of (71*100)? not sure why its a 7.1, am i missing something?

Reply 3

AlmostNotable

Original post by kc006

wait isnt the cube root of (7100) the same as cube root of (71*100)? not sure why its a 7.1, am i missing something?

71*100=7.1*1000

Reply 4

kc006

Original post by AlmostNotable

71*100=7.1*1000

jesus christ im screwed for tomorrow

Reply 5

timelizard

Original post by kc006

wait isnt the cube root of (7100) the same as cube root of (71*100)? not sure why its a 7.1, am i missing something?

while youre right, technically

but that doesn't help answer the question. We need to get cube root of 7100 into a form where it can be substituted into the expansion. Also, our x needs to be less than 8/9
i.e. we need to write cube root (7100) in a similar form to cube root (8-9x)

while 7100 is 71*100, 100 is not a cube root. by dividing by taking out 1000 you can write it as 10*cube root (7.1)
We now need to make 8-9x=7.1
we get x =0.1
so,
cube root 7100 = 10[cube root(8-9x)] when x = 0.1

to answer the question, sub in 0.1 to your expansion that youve found, then multiply by 10

does that make sense?