SOLUTION: Write each expression below in simplest radical form. SHOW YOUR STEPS. √4x^8 I'm pretty sure that the answer is 2x^4√, but how do I show the steps? I'd apprecia

Algebra ->  Radicals -> SOLUTION: Write each expression below in simplest radical form. SHOW YOUR STEPS. √4x^8 I'm pretty sure that the answer is 2x^4√, but how do I show the steps? I'd apprecia      Log On


   

Question 375116: Write each expression below in simplest radical form. SHOW YOUR STEPS.
√4x^8
I'm pretty sure that the answer is 2x^4√, but how do I show the steps?
I'd appreciate some help! Thank you! :)
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

sqrt%284%2Ax%5E8%29 Start with the given expression.


sqrt%284%2Ax%5E2%2Ax%5E2%2Ax%5E2%2Ax%5E2%29 Factor x%5E8 into x%5E2%2Ax%5E2%2Ax%5E2%2Ax%5E2


sqrt%284%29%2Asqrt%28x%5E2%29%2Asqrt%28x%5E2%29%2Asqrt%28x%5E2%29%2Asqrt%28x%5E2%29 Break up the square root using the identity sqrt%28A%2AB%29=sqrt%28A%29%2Asqrt%28B%29.


2%2Asqrt%28x%5E2%29%2Asqrt%28x%5E2%29%2Asqrt%28x%5E2%29%2Asqrt%28x%5E2%29 Take the square root of 4 to get 2.


2%2Ax%2Ax%2Ax%2Ax Take the square root of x%5E2 to get x.


2x%5E4 Rearrange and multiply the terms.

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Answer:


So sqrt%284%2Ax%5E8%29 simplifies to 2x%5E4


In other words, sqrt%284%2Ax%5E8%29=2x%5E4 where x is nonnegative.



If you need more help, email me at jim_thompson5910@hotmail.com

Also, feel free to check out my tutoring website

Jim