SOLUTION: simplilfy: √[144x^10y^12z^18]

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Question 195063: simplilfy: √[144x^10y^12z^18]
Found 2 solutions by RAY100, jim_thompson5910:
Answer by RAY100(1637) About Me  (Show Source):
You can put this solution on YOUR website!
sqrt ( 144 x^10 y^12 z^18
.
sqrt144 * sqrt x^10 *sqrt y^12 *sqrt z^18
.
12 * x^5 *y^6 *z^9

Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

sqrt%28144%2Ax%5E10%2Ay%5E12%2Az%5E18%29 Start with the given expression.


sqrt%28144%2Ax%5E2%2Ax%5E2%2Ax%5E2%2Ax%5E2%2Ax%5E2%2Ay%5E12%2Az%5E18%29 Factor x%5E10 into x%5E2%2Ax%5E2%2Ax%5E2%2Ax%5E2%2Ax%5E2


Factor y%5E12 into y%5E2%2Ay%5E2%2Ay%5E2%2Ay%5E2%2Ay%5E2%2Ay%5E2


Factor z%5E18 into z%5E2%2Az%5E2%2Az%5E2%2Az%5E2%2Az%5E2%2Az%5E2%2Az%5E2%2Az%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 144 to get 12.


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


Take the square root of y%5E2 to get y.


12%2Ax%2Ax%2Ax%2Ax%2Ax%2Ay%2Ay%2Ay%2Ay%2Ay%2Ay%2Az%2Az%2Az%2Az%2Az%2Az%2Az%2Az%2Az Take the square root of z%5E2 to get z.


12x%5E5y%5E6z%5E9 Rearrange and multiply the terms.

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Answer:


So sqrt%28144%2Ax%5E10%2Ay%5E12%2Az%5E18%29 simplifies to 12x%5E5y%5E6z%5E9


In other words, sqrt%28144%2Ax%5E10%2Ay%5E12%2Az%5E18%29=12x%5E5y%5E6z%5E9 where every variable is non-negative.