SOLUTION: 3. Simplify: √[144x10y12z18]

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Question 118228: 3. Simplify:
√[144x10y12z18]


Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
sqrt%28144%2Ax%5E10y%5E12z%5E18%29 Start with the given expression
Factor x%5E10y%5E12z%5E18 into

Break up the square root using the identity sqrt%28x%2Ay%29=sqrt%28x%29%2Asqrt%28y%29

Take the square root of the perfect square 144 to get 12

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 the perfect squares x%5E2, y%5E2 and z%5E2 to get x, y and z

12%2Ax%5E5y%5E6z%5E9 Multiply the common terms



So sqrt%28144%2Ax%5E10y%5E12z%5E18%29 simplifies to 12%2Ax%5E5y%5E6z%5E9



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Here's another way to do it


sqrt%28144%2Ax%5E10y%5E12z%5E18%29 Start with the given expression


%28144%2Ax%5E10y%5E12z%5E18%29%5E%281%2F2%29 Rewrite the radical expression into an exponential expression


%28%28144%5E1%29%2Ax%5E10y%5E12z%5E18%29%5E%281%2F2%29 Rewrite 144 as 144%5E1


Distribute the outer exponent


144%5E%281%2F2%29%2Ax%5E%2810%2F2%29y%5E%2812%2F2%29z%5E%2818%2F2%29 Multiply the exponents


144%5E%281%2F2%29%2Ax%5E5y%5E6z%5E9 Simplify


sqrt%28144%29%2Ax%5E5y%5E6z%5E9 Rewrite 144%5E%281%2F2%29 as sqrt%28144%29


12%2Ax%5E5y%5E6z%5E9 Take the square root of the perfect square 144 to get 12


So sqrt%28144%2Ax%5E10y%5E12z%5E18%29 simplifies to 12%2Ax%5E5y%5E6z%5E9