SOLUTION: simplify the square root of 40x4y7

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Question 303166: simplify the square root of 40x4y7
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

sqrt%2840%2Ax%5E4%2Ay%5E7%29 Start with the given expression.


sqrt%284%2A10%2Ax%5E4%2Ay%5E7%29 Factor 40 into 4%2A10


sqrt%284%2A10%2Ax%5E2%2Ax%5E2%2Ay%5E7%29 Factor x%5E4 into x%5E2%2Ax%5E2


sqrt%284%2A10%2Ax%5E2%2Ax%5E2%2Ay%5E2%2Ay%5E2%2Ay%5E2%2Ay%29 Factor y%5E7 into y%5E2%2Ay%5E2%2Ay%5E2%2Ay


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


Take the square root of 4 to get 2.


2%2Asqrt%2810%29%2Ax%2Ax%2Asqrt%28y%5E2%29%2Asqrt%28y%5E2%29%2Asqrt%28y%5E2%29%2Asqrt%28y%29 Take the square root of x%5E2 to get x.


2%2Asqrt%2810%29%2Ax%2Ax%2Ay%2Ay%2Ay%2Asqrt%28y%29 Take the square root of y%5E2 to get y.


2x%5E2y%5E3%2Asqrt%2810y%29 Rearrange and multiply the terms.

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Answer:


So sqrt%2840%2Ax%5E4%2Ay%5E7%29 simplifies to 2x%5E2y%5E3%2Asqrt%2810y%29


In other words, sqrt%2840%2Ax%5E4%2Ay%5E7%29=2x%5E2y%5E3%2Asqrt%2810y%29 where every variable is non-negative.