SOLUTION: How would I simplify √³√5 I don't get how to simplify square roots in side of another square root.

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Question 244765: How would I simplify √³√5
I don't get how to simplify square roots in side of another square root.
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
Old Stuff
Hint: Remember that root%283%2Cx%29=%28x%29%5E%281%2F3%29%5E%22%22. In addition, sqrt%28x%29=%28x%29%5E%281%2F2%29%5E%22%22. Use these two equations along with the identity %28x%5Ey%29%5Ez=x%5E%28yz%29 to simplify the problem. Let me know if this hint helps or not. If not, then repost or ask me.

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New Stuff

root%283%2Csqrt%285%29%29 Start with the given expression.


root%283%2C5%5E%281%2F2%29%5E%22%22%29 Rewrite sqrt%285%29 as 5%5E%281%2F2%29%5E%22%22 using the property sqrt%28x%29=%28x%29%5E%281%2F2%29%5E%22%22


%285%5E%281%2F2%29%29%5E%281%2F3%29 Convert root%283%2C5%5E%281%2F2%29%5E%22%22%29 to %285%5E%281%2F2%29%29%5E%281%2F3%29 using the property root%283%2Cx%29=%28x%29%5E%281%2F3%29%5E%22%22


5%5E%28%281%2F2%29%2A%281%2F3%29%29%5E%22%22 Multiply the exponents using the idea that %28x%5Ey%29%5Ez=x%5E%28yz%29


5%5E%28%281%2A1%29%2F%282%2A3%29%29%5E%22%22 Combine the fractions.


5%5E%281%2F6%29%5E%22%22 Multiply


root%286%2C5%29 Convert back to radical notation


So root%283%2Csqrt%285%29%29=root%286%2C5%29