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sqrt (320x^4) =sqrt [(8)(8)(5)(x^2)(x^20] =

8sqrt5 x^2
by Level 5 User (12.9k points)
Simplify to the forth power
√(320x) = √(320)*√(x)
320 = 2*160 = 2*2*80 = 2*2*2*40 = 2*2*2*2*20 = 2*2*2*2*20 = (2^4)(20)
320 = (2^4)(20)
√(320x) = √(320)*√(x) = √(2^4)(20)*√(x) = √(2^4)*√(20)*√(x)
√(2^4)*√(20)*√(x) = √(2^4)*√(20x)
√(2^4)*√(20x)
√(2^4) = √(16)
√(16) = ±4 (plus or minus 4)
So..
√(2^4)*√(20x) = √(16)*√(20x)
√(16)*√(20x) = ±4√(20x)
√(320x) = ±4√(20x)
Note: Do not forget to place ± (plus or minus) when simplifing radicals otherwise the simplified radical is incorrect.
by Level 1 User (460 points)

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