SOLUTION: for all x > or equal to y > or equal to, the sqaure root of 250x9y4 The computer program i am using for compass practice says to find the square root of x9 which is x4 times the

Algebra ->  Exponents -> SOLUTION: for all x > or equal to y > or equal to, the sqaure root of 250x9y4 The computer program i am using for compass practice says to find the square root of x9 which is x4 times the      Log On


   

Question 246704: for all x > or equal to y > or equal to, the sqaure root of 250x9y4
The computer program i am using for compass practice says to find the square root of x9 which is x4 times the square root of x. they then say that it is equal to 5x4 times y4 times the square root of 10x. why is this so? I don't understand why they are equal....
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

sqrt%28250%2Ax%5E9%2Ay%5E4+%29 Start with the given expression.


sqrt%2825%2A10%2Ax%5E9%2Ay%5E4+%29 Factor 250 into 25%2A10


sqrt%2825%2A10%2Ax%5E2%2Ax%5E2%2Ax%5E2%2Ax%5E2%2Ax%2Ay%5E4+%29 Factor x%5E9 into x%5E2%2Ax%5E2%2Ax%5E2%2Ax%5E2%2Ax


sqrt%2825%2A10%2Ax%5E2%2Ax%5E2%2Ax%5E2%2Ax%5E2%2Ax%2Ay%5E2%2Ay%5E2%29 Factor y%5E4+ into y%5E2%2Ay%5E2


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


Take the square root of 25 to get 5.


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


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


5x%5E4y%5E2%2Asqrt%2810x%29 Rearrange and multiply the terms.

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Answer:


So sqrt%28250%2Ax%5E9%2Ay%5E4+%29 simplifies to 5x%5E4y%5E2%2Asqrt%2810x%29


In other words, sqrt%28250%2Ax%5E9%2Ay%5E4+%29=5x%5E4y%5E2%2Asqrt%2810x%29 where every variable is non-negative.