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)#

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Notice that #18 = 2*3*3 = 2*3^2#

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Note also that #3x^4 >= 0# for all #x in RR#

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Hence:

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

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