SOLUTION: Simplify {{{sqrt(49*x^12*y^4*z^8)}}}

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Question 147677: Simplify sqrt%2849%2Ax%5E12%2Ay%5E4%2Az%5E8%29
Answer by jim_thompson5910(21667) About Me  (Show Source):
You can put this solution on YOUR website!

sqrt%2849%2Ax%5E12%2Ay%5E4%2Az%5E8%29 Start with the given expression.


sqrt%28%287%29%5E2%2Ax%5E12%2Ay%5E4%2Az%5E8%29 Rewrite 49 as %287%29%5E2


sqrt%28%287%29%5E2%2A%28x%5E6%29%5E2%2Ay%5E4%2Az%5E8%29 Rewrite x%5E12 as %28x%5E6%29%5E2


sqrt%28%287%29%5E2%2A%28x%5E6%29%5E2%2A%28y%5E2%29%5E2%2Az%5E8%29 Rewrite y%5E4 as %28y%5E2%29%5E2


sqrt%28%287%29%5E2%2A%28x%5E6%29%5E2%2A%28y%5E2%29%5E2%2A%28z%5E4%29%5E2%29 Rewrite z%5E8 as %28z%5E4%29%5E2


sqrt%28%287%29%5E2%29%2Asqrt%28%28x%5E6%29%5E2%29%2Asqrt%28%28y%5E2%29%5E2%29%2Asqrt%28%28z%5E4%29%5E2%29 Break up the square root using the identity sqrt%28x%2Ay%29=sqrt%28x%29%2Asqrt%28y%29


7%2Ax%5E6%2Ay%5E2%2Az%5E4 Evaluate each square root. Notice how the squares and the square roots cancel out and we're left with the terms that are in the parenthesis.


So sqrt%2849%2Ax%5E12%2Ay%5E4%2Az%5E8%29 simplifies to 7%2Ax%5E6%2Ay%5E2%2Az%5E4.


In other words, sqrt%2849%2Ax%5E12%2Ay%5E4%2Az%5E8%29=7%2Ax%5E6%2Ay%5E2%2Az%5E4 where every variable is positive.