Question

V = Radical

The expression:

V2(V5-12V3)-V3(V8-2V30) can be written in simplest form aVb-cVd, where a, b, c ,d are all positive integers. The value of a + b + c + d is ________.

So after solving all this out, I arrived at 7V10 - 14V6. That - is beside the 14, and Im only supposed to have positive integers, so does that negative sign mean anything at all *question mark* --Sorry accidentally pressed this button on keyboard, now Im getting all these french letters, so cant paste a question mark.

Answer 1

what the negative sign means is c is negative.

Answer 2

But all a,b,c and d are supposed to be positive integers, and I looked over this again, and its supposed to simplify into aVb-cVd, so that means that the negative sign is supposed to be there, but the integer C is not negative.

Answer 3

√2(√5-12√3)-√3(√8-2√30)
= √10 - 12√6 - √24 + 2√90
= √10 - 12√6 - 2√6 + 6√10
= 7√10 - 14√6

which is what you got.

comparing this to a√b - c√d
a=7 , b = 10 , c = -14, and d = 6
so
a+b+c+d = 7+10-14+6 = 9

Trust yourself!