Question

Dont know if the radicals will show up..

2ã3(ã243-2)-ã2(5+7ã2) Can be expanded and simplified to the form
p + qã2 + rã3. the value of p + q + r is_____

First I simplified the V243 and I got 9V3

2V3(9V3-2)-V2(5+7V2)
18V9-4V3-5V2-7V2
54-4V3-5V2-7V2
54-4V3-12V2

But this just doesnt work out, and i have no idea what ive done wrong.

Answer 1

2√3(√243-2)-√2(5+7√2)
= 2√729 - 4√3 - 5√2 - 7√4
= 54 - 4√3 - 5√2 - 14
= 40 - 4√3 - 5√2

comparing this with
p + q√2 + r√3
p=40, q= -5, and r = -4

so p+q+r = 40-5-4 = 31

check my arithmetic.

Answer 2

Ok, so I missed out the 4, and ended up writing 7V2. That missing out the 4 messed up everything, and yup you are right, thanks a bunch =D