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

1 Answer
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