SOLUTION: Hi, Could you pls help me with this question: Simplify completely : {sqrt(24 x^6)} Thanks H.H

Algebra ->  Graphs -> SOLUTION: Hi, Could you pls help me with this question: Simplify completely : {sqrt(24 x^6)} Thanks H.H      Log On


   

Question 592714: Hi,
Could you pls help me with this question:
Simplify completely : {sqrt(24 x^6)}
Thanks
H.H
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

sqrt%2824%2Ax%5E6%29 Start with the given expression.


sqrt%284%2A6%2Ax%5E6%29 Factor 24 into 4%2A6


sqrt%284%2A6%2Ax%5E2%2Ax%5E2%2Ax%5E2%29 Factor x%5E6 into x%5E2%2Ax%5E2%2Ax%5E2


sqrt%284%29%2Asqrt%286%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%286%29%2Asqrt%28x%5E2%29%2Asqrt%28x%5E2%29%2Asqrt%28x%5E2%29 Take the square root of 4 to get 2.


2%2Asqrt%286%29%2Ax%2Ax%2Ax Take the square root of x%5E2 to get x.


2x%5E3%2Asqrt%286%29 Rearrange and multiply the terms.

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Answer:


So sqrt%2824%2Ax%5E6%29 simplifies to 2x%5E3%2Asqrt%286%29


In other words, sqrt%2824%2Ax%5E6%29=2x%5E3%2Asqrt%286%29 where x is non-negative.