SOLUTION: Simplify the radical expression: {{{ sqrt( 125x^5y^2z^4) }}}

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Question 253918: Simplify the radical expression: +sqrt%28+125x%5E5y%5E2z%5E4%29+
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

sqrt%28125%2Ax%5E5%2Ay%5E2%2Az%5E4%29 Start with the given expression.


sqrt%2825%2A5%2Ax%5E5%2Ay%5E2%2Az%5E4%29 Factor 125 into 25%2A5


sqrt%2825%2A5%2Ax%5E2%2Ax%5E2%2Ax%2Ay%5E2%2Az%5E4%29 Factor x%5E5 into x%5E2%2Ax%5E2%2Ax


sqrt%2825%2A5%2Ax%5E2%2Ax%5E2%2Ax%2Ay%5E2%2Az%5E2%2Az%5E2%29 Factor z%5E4 into z%5E2%2Az%5E2


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


Take the square root of 25 to get 5.


5%2Asqrt%285%29%2Ax%2Ax%2Asqrt%28x%29%2Asqrt%28y%5E2%29%2Asqrt%28z%5E2%29%2Asqrt%28z%5E2%29 Take the square root of x%5E2 to get x.


5%2Asqrt%285%29%2Ax%2Ax%2Asqrt%28x%29%2Ay%2Asqrt%28z%5E2%29%2Asqrt%28z%5E2%29 Take the square root of y%5E2 to get y.


5%2Asqrt%285%29%2Ax%2Ax%2Asqrt%28x%29%2Ay%2Az%2Az Take the square root of z%5E2 to get z.


5x%5E2yz%5E2%2Asqrt%285x%29 Rearrange and multiply the terms.

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Answer:


So sqrt%28125%2Ax%5E5%2Ay%5E2%2Az%5E4%29 simplifies to 5x%5E2yz%5E2%2Asqrt%285x%29


In other words, sqrt%28125%2Ax%5E5%2Ay%5E2%2Az%5E4%29=5x%5E2yz%5E2%2Asqrt%285x%29 where every variable is non-negative.