SOLUTION: Simplify Sqrt[121x^12y^16z^6] Thanks for the help with this. :)

Algebra ->  Radicals -> SOLUTION: Simplify Sqrt[121x^12y^16z^6] Thanks for the help with this. :)      Log On


   

Question 178102: Simplify
Sqrt[121x^12y^16z^6]
Thanks for the help with this. :)
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

sqrt%28121%2Ax%5E12%2Ay%5E16%2Az%5E6%29 Start with the given expression.


sqrt%28121%2Ax%5E2%2Ax%5E2%2Ax%5E2%2Ax%5E2%2Ax%5E2%2Ax%5E2%2Ay%5E16%2Az%5E6%29 Factor x%5E12 into x%5E2%2Ax%5E2%2Ax%5E2%2Ax%5E2%2Ax%5E2%2Ax%5E2 (note: there are 6 x%5E2 terms)


Factor y%5E16 into y%5E2%2Ay%5E2%2Ay%5E2%2Ay%5E2%2Ay%5E2%2Ay%5E2%2Ay%5E2%2Ay%5E2 (note: there are 8 y%5E2 terms)


Factor z%5E6 into z%5E2%2Az%5E2%2Az%5E2 (note: there are 3 z%5E2 terms)


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


Take the square root of 121 to get 11.


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


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


11%2Ax%2Ax%2Ax%2Ax%2Ax%2Ax%2Ay%2Ay%2Ay%2Ay%2Ay%2Ay%2Ay%2Ay%2Az%2Az%2Az Take the square root of z%5E2 to get z.


11x%5E6y%5E8z%5E3 Multiply and simplify.

==================================================

Answer:


So sqrt%28121%2Ax%5E12%2Ay%5E16%2Az%5E6%29 simplifies to 11x%5E6y%5E8z%5E3


In other words, sqrt%28121%2Ax%5E12%2Ay%5E16%2Az%5E6%29=11x%5E6y%5E8z%5E3 where every variable is positive.