How do you evalaute #\sqrt { 45} \times \sqrt { 64}#?

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Answer 1 · 2018-05-05T09:55:20

#24sqrt5#

#sqrt45 times sqrt64 = sqrt(9*5) times sqrt(8*8) = 3sqrt5 times8 = 24sqrt5#

Answer 2 · 2018-05-05T10:01:49

#24*\sqrt(5)#

#\sqrt(45)*\sqrt(64)#

Write both numbers as a product of prime numbers .
(unique factorization).

#45=5*9=5*3*3#
#64=2*32=2*2*16=2*2*2*8=2*2*2*2*4=#
#=2*2*2*2*2*2=2^6#

#\sqrt(45)*\sqrt(64)=#

#=\sqrt(5*3*3)*\sqrt(2^6)=#

#=\sqrt(5*3^2)*2^(6/2)=#

#=\sqrt(5)*\sqrt(3^2)*2^3=#

#=\sqrt(5)*3*8=#

#=24*\sqrt(5)#