SOLUTION: the square root of 25x^2y^6z

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Question 547819: the square root of 25x^2y^6z
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

sqrt%2825%2Ax%5E2%2Ay%5E6%2Az%29 Start with the given expression.


sqrt%2825%2Ax%5E2%2Ay%5E2%2Ay%5E2%2Ay%5E2%2Az%29 Factor y%5E6 into y%5E2%2Ay%5E2%2Ay%5E2


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


5%2Asqrt%28x%5E2%29%2Asqrt%28y%5E2%29%2Asqrt%28y%5E2%29%2Asqrt%28y%5E2%29%2Asqrt%28z%29 Take the square root of 25 to get 5.


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


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


5xy%5E3%2Asqrt%28z%29 Rearrange and multiply the terms.

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Answer:


So sqrt%2825%2Ax%5E2%2Ay%5E6%2Az%29 simplifies to 5xy%5E3%2Asqrt%28z%29


In other words, sqrt%2825%2Ax%5E2%2Ay%5E6%2Az%29=5xy%5E3%2Asqrt%28z%29 where every variable is non-negative.