How do you simplify #2* sqrt(-1/6) + sqrt(-4/3) #?

1 Answer
Mar 25, 2016

Answer:

#isqrt(3)/3(sqrt(2)+4 )#

Explanation:

Simplify: #2*sqrt(-1/6)+sqrt(-4/3)#
#2*isqrt(1/6)+isqrt(4/3)#
#2/sqrt(2)*isqrt(1/3)+isqrt(4/3)#
#(2i)[1/(sqrt(2)sqrt(3))+sqrt(4)/sqrt(3)] = 2i(1+2sqrt(2))/(sqrt(6)#
Multiply top and bottom by #sqrt(6)#
#2i(1+2sqrt(2))/(sqrt(6))*sqrt(6)/sqrt(6)= 2i(sqrt(6)+2sqrt(3)sqrt(2)*sqrt(2))/(sqrt(6)*sqrt(6)#

#2i(sqrt(2)sqrt(3)+4sqrt(3))/(6)=isqrt(3)/3(sqrt(2)+4 )#