How do you simplify #5sqrt(54)# ?

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Answer 1 · 2017-03-05T01:14:31

#5 sqrt(54) = 15sqrt(6)#

Note that if #a, b >= 0# we have:

#sqrt(ab) = sqrt(a)sqrt(b)#

Factor #54# to identify square factors:

#54 = 2*3^3 = 3^2*6#

Hence:

#5 sqrt(54) = 5 sqrt(3^2 * 6) = 5sqrt(3^2)sqrt(6) = 5*3sqrt(6) = 15sqrt(6)#

This is the simplest form of the square root.