SOLUTION: square root of 20 times the cubed root of 135 solve please

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Question 918849: square root of 20 times the cubed root of 135 solve please



Found 2 solutions by KMST, Alan3354:
Answer by KMST(5328) About Me  (Show Source):
You can put this solution on YOUR website!
sqrt%2820%2A%28root%283%2C+135%29%29%29 ?

The factorization of each number will tell you if you can simplify.
135=27%2A5=3%2A3%2A3%2A5=3%5E3%2A5 and 20=4%2A5=2%2A2%2A5=2%5E2%2A5 so there is room for some simplifications.
What is the simplest (or more convenient) way to express it?
Would you like to show your work with roots, or with fractional exponents?

WITH ROOTS:
sqrt%2820%2A%28root%283%2C+135%29%29%29=sqrt%284%2A5%2A%28root%283%2C27%2A5%29%29%29=sqrt%284%29%2Asqrt%285%29%2Asqrt%28%28root%283%2C27%29%2Aroot%283%2C5%29%29%29=2%2Asqrt%285%29%2Asqrt%28%283%2Aroot%283%2C5%29%29%29=2%2Asqrt%285%29%2Asqrt%283%29%2Asqrt%28root%283%2C5%29%29=2%2Asqrt%285%29%2Asqrt%283%29%2Aroot%286%2C5%29=2%2Asqrt%283%29%2Asqrt%285%29%2Aroot%286%2C5%29=2%2Asqrt%283%29%2Aroot%286%2C5%5E3%29%2Aroot%286%2C5%29=2%2Asqrt%283%29%2Aroot%286%2C5%5E3%2A5%29=2%2Asqrt%283%29%2Aroot%286%2C5%5E4%29=2%2Asqrt%283%29%2Aroot%283%2C5%5E2%29=2%2Asqrt%283%29%2Aroot%283%2C25%29

WITH FRACTIONAL EXPONENTS:
sqrt%2820%2A%28root%283%2C+135%29%29%29=%2820%2A135%5E%281%2F3%29%29%5E%281%2F2%29=%2820%29%5E%281%2F2%29%2A%28135%5E%281%2F3%29%29%5E%281%2F2%29=%282%5E2%2A5%29%5E%281%2F2%29%2A%28%283%5E3%2A5%29%5E%281%2F3%29%29%5E%281%2F2%29 ==
2%2A5%5E%281%2F2%29%2A%283%2A5%5E%281%2F3%29%29%5E%281%2F2%29%29==2%2A5%5E%22%281%2F2%29%22%2A3%5E%22%281%2F2%29%22%2A5%5E%22%281%2F6%29%22=2%2A3%5E%22%281%2F2%29%22%2A5%5E%28%28%221%2F2%22%2B%221%2F6%22%29%29=2%2A3%5E%22%281%2F2%29%22%2A5%5E%22%284%2F6%29%22=2%2A3%5E%22%281%2F2%29%22%2A5%5E%22%282%2F3%29%22

Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
It's not cubed root. It's cube root.