SOLUTION: Can someone please help me with this: Simplify the expression. 3(square root)8 (times) 3(square root) 64

Algebra ->  Square-cubic-other-roots -> SOLUTION: Can someone please help me with this: Simplify the expression. 3(square root)8 (times) 3(square root) 64      Log On


   

Question 201122: Can someone please help me with this:
Simplify the expression.
3(square root)8 (times) 3(square root) 64
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
Is the expression root%283%2C8%29%2Aroot%283%2C64%29 ???


If so, then...


root%283%2C8%29%2Aroot%283%2C64%29 Start with the given expression.


root%283%2C2%5E3%29%2Aroot%283%2C64%29 Factor 8 to get 2%5E3


root%283%2C2%5E3%29%2Aroot%283%2C4%5E3%29 Factor 64 to get 4%5E3


2%2Aroot%283%2C4%5E3%29 Evaluate the cube root of 2%5E3 to get 2


Note: root%283%2Cx%5E3%29=x for any value of "x"


2%2A4 Evaluate the cube root of 4%5E3 to get 4


8 Multiply


So root%283%2C8%29%2Aroot%283%2C64%29=8


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Or....

Is the expression 3%2Asqrt%288%29%2A3%2Asqrt%2864%29 ???


%283%2Asqrt%288%29%29%2A%283%2Asqrt%2864%29%29 Start with the given expression.


3%2A3%2Asqrt%288%29%2Asqrt%2864%29 Rearrange the terms.


3%2A3%2Asqrt%284%2A2%29%2Asqrt%2864%29 Factor 8 into 4*2


3%2A3%2Asqrt%284%29%2Asqrt%282%29%2Asqrt%2864%29 Break up the square root.


3%2A3%2A2%2Asqrt%282%29%2Asqrt%2864%29 Take the square root of 4 to get 2


3%2A3%2A2%2Asqrt%282%29%2A8 Take the square root of 64 to get 8


3%2A3%2A2%2A8%2Asqrt%282%29 Rearrange the terms.


144%2Asqrt%282%29 Multiply


So %283%2Asqrt%288%29%29%2A%283%2Asqrt%2864%29%29=144%2Asqrt%282%29