Simplify each expression (9-4√3)(2 + 8√3)?

Question

a -78 + 64√3

b -54 + 64√3

c 11 + 4√3

Can you help me with this one too, please:

(exponent 4 in the sqrt sign) √48m^7y^9w^4

a. 4m(^3) y(^4) w²√3m(^3) y

b. 4my²|w| (exponent 4 in sqrt sign)√3m(^3) y

c. 2my²|w| (exponent 4 in sqrt sign)√3m(^3) y

Answer 1

cant find the sq root sign so i will use a "?"

expanding this out you get 9*2=18; -4?3*2=-8?3; 9*8?3=72?3; -4?3*8?3=-96  (multiply 2 SAME sq. roots and you get THAT number so the last one is actually -4*8*3)

adding these together get you A as your answer

for the second one you can pull out two at a time from under the sq root and count them as one (pull out w^4 and get w^2)

Answer 2

(1) (9-4√3)(2 + 8√3)?

Multiply it out to get

(9-4√3)(2 + 8√3) = 18 - 32*3 + (72 - 8)*sqrt(3)

= - 78 + 64*sqrt(3)

(2) Assuming that √48m^7y^9w^4 = sqrt(48m^7y^9w^4)

= sqrt[16*3*m^(6)*m*y^(8)*y*w^(4)]

= 4*m^(3)*y^(4)*w^(2)*sqrt(3*m*y)