What is the square root of -16 times the square root of -10? Algebra Radicals and Geometry Connections Multiplication and Division of Radicals 1 Answer Bill Jorgensen May 19, 2018 #-4sqrt(10)# Explanation: By definition of imaginary numbers: #i = sqrt(-1)# #sqrt(-16) = 4*sqrt(-1) = 4i# #sqrt(-10) = sqrt(10)*sqrt(-1) = sqrt(10)i# #i^2=i*i= sqrt(-1) * sqrt(-1) = (sqrt(-1))^2 = -1 # so: #4i * sqrt(10)i = 4sqrt(10)* i^2 = 4sqrt(10)* (-1) = -4sqrt(10)# Answer link Related questions How do you simplify #\frac{2}{\sqrt{3}}#? How do you multiply and divide radicals? How do you rationalize the denominator? What is Multiplication and Division of Radicals? How do you simplify #7/(""^3sqrt(5)#? How do you multiply #(sqrt(a) +sqrt(b))(sqrt(a)-sqrt(b))#? How do you rationalize the denominator for #\frac{2x}{\sqrt{5}x}#? Do you always have to rationalize the denominator? How do you simplify #sqrt(5)sqrt(15)#? How do you simplify #(7sqrt(13) + 2sqrt(6))(2sqrt(3)+3sqrt(6))#? See all questions in Multiplication and Division of Radicals Impact of this question 1334 views around the world You can reuse this answer Creative Commons License