SOLUTION: I keep confusing myself with this problem. worksheet states please simplify each of the following. sqrt(3x^6)* sqrt(27x^13)=

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Question 167645: I keep confusing myself with this problem. worksheet states please simplify each of the following.
sqrt(3x^6)* sqrt(27x^13)=
Found 3 solutions by stanbon, jim_thompson5910, gonzo:
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website!
simplify each of the following.
sqrt(3x^6)* sqrt(27x^13)=
= sqrt[81x^19]
= 9*x^9*sqrt(x)
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Cheers,
Stan H.

Answer by jim_thompson5910(35256)   (Show Source):
You can put this solution on YOUR website!

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Answer:

So

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Here are some side notes

1) All variables are positive so this means that

2) To multiply variables with exponents (the same variables) simply add the exponents

3) The goal to simplify this is to break 19 into 18+1 where 18 is a multiple of 2 (that way, we can take the square root)

Answer by gonzo(654)   (Show Source):
You can put this solution on YOUR website!
***** equation 1 *****
since = , this becomes:

since a*b*c*d = a*c*b*d, this becomes:

since , this becomes:

simplifying, this becomes:
***** equation 2 *****
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to prove the answer is correct, let x be any number that can be easily handled by your calculator.
for example:
let x = 3
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equation 1 becomes:

this becomes:

this becomes:

this becomes:
306827.6044.
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equation 2 becomes:

this becomes:

this becomes:

this becomes:

this becomes:
306827.6044
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the answers come out the same so equation 1 is equivalent to equation 2.