How do you simplify #sqrt(18 x^8)#?

1 Answer
George C.
Mar 10, 2016

#sqrt(18x^8) = 3sqrt(2)x^4#

Explanation:

If #a, b >= 0# then #sqrt(ab) = sqrt(a)sqrt(b)#

#color(white)()#
Notice that #18 = 2*3*3 = 2*3^2#

#color(white)()#
Note also that #3x^4 >= 0# for all #x in RR#

#color(white)()#
Hence:

#sqrt(18x^8) = sqrt((3x^4)^2*2) = sqrt((3x^4)^2)sqrt(2) = 3x^4sqrt(2) = 3sqrt(2)x^4#

Related questions
See all questions in Simplification of Radical Expressions
Impact of this question
1515 views around the world
You can reuse this answer
Creative Commons License