square root help?

Question

(5-3sqrt[-48]) (2-4sqrt[-27])

im lost...

Answer 1

Hai rosecrashers1365,

This is a problem of "Complex Numbers"(numbers involving both a real part & an imaginary part).

Consider,
(5-3sqrt[48])(2-4sqrt[-27])
= {5-3sqrt[(3)(16)]}{2-4sqrt[(-)...
= {5-3(4)[sqrt(3)]}{2-4(3)sqrt[(...
= {5-12[sqrt(3)]}{2-12(i)sqrt(3)...

This is of the form, (a-c)(b-ic), where,
a= 5;
b = 2;
c=12[sqrt(3)];
i = sqrt(-1), an imaginary number.

Answer 2

[5-3sqrt(-48)] = 5 - 3 x 4sqrt3 = 5 - 12 i sqrt3

2 - 4sqrt(-27) = 2 - 4 x 3 i sqrt3 = 2 - 12 i sqrt3

Multiplying both,

10 - 24 i sqrt3 - 60 i sqrt3 + 144 i^2 x 3

= 10 - 84 i sqrt3 - 432 (i^2 is -1)

= - 84 i sqrt3 - 432

Answer 3

Well..here's my solution for this:

[5-3sqrt(-48)] [2-4sqrt(-27)]
[5-3sqrt(16*-3)] [2-4sqrt(9*-3)]
[5-12sqrt(-3)] [2-12sqrt(-3)]
10 - 60sqrt(-3) - 24sqrt(-3) - 24sqrt(-3) +144(-3)
10 - 84sqrt(-3) - 432
-84sqrt(-3) - 432
since sqrt(-1) = i, then...
-84isqrt(3) - 432