SOLUTION: The problem I am trying to simplify this radical expression: {{{sqrt(98x^4y^6z^2)}}}

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Question 179904: The problem I am trying to simplify this radical
expression:
sqrt%2898x%5E4y%5E6z%5E2%29
Answer by Edwin McCravy(6935) About Me  (Show Source):
You can put this solution on YOUR website!


sqrt%2898x%5E4y%5E6z%5E2%29

Break 98 down into into primes: 98=2%2A49=2%2A7%2A7

Break x%5E4 down into primes: x%2Ax%2Ax%2Ax

Break y%5E6 down into primes: y%2Ay%2Ay%2Ay%2Ay%2Ay

Break z%5E2 down into primes: z%2Az

So we have

sqrt%282%2A7%2A7%2Ax%2Ax%2Ax%2Ax%2Ay%2Ay%2Ay%2Ay%2Ay%2Ay%2Az%2Az%29

Now use parentheses to group all possible pairs 
of like factors:

sqrt%282%2A%287%2A7%29%2A%28x%2Ax%29%2A%28x%2Ax%29%2A%28y%2Ay%29%2A%28y%2Ay%29%2A%28y%2Ay%29%2A%28z%2Az%29%29

sqrt%282%2A7%5E2%2Ax%5E2%2Ax%5E2%2Ay%5E2%2Ay%5E2%2Ay%5E2%2Az%5E2%29

Every square comes out as just its base.  Only
the 2 at the beginning which didn't pair up will
stay under the radical:

7%2Ax%2Ax%2Ay%2Ay%2Ay%2Az%2Asqrt%282%29

Simplify:

7%2Ax%5E2%2Ay%5E3%2Az%2Asqrt%282%29

7x%5E2y%5E3z%2Asqrt%282%29

Edwin