SOLUTION: Write the expression in simplest form using the properties of exponents and radicals. Assume all variables are positive √25x^5y^4

Algebra ->  Square-cubic-other-roots -> SOLUTION: Write the expression in simplest form using the properties of exponents and radicals. Assume all variables are positive √25x^5y^4       Log On


   

Question 178027: Write the expression in simplest form using the properties of exponents and radicals. Assume all variables are positive
√25x^5y^4

Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

sqrt%2825%2Ax%5E5%2Ay%5E4%29 Start with the given expression.


sqrt%2825%2Ax%5E2%2Ax%5E2%2Ax%2Ay%5E4%29 Factor x%5E5 into x%5E2%2Ax%5E2%2Ax


sqrt%2825%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.


5%2Asqrt%28x%5E2%29%2Asqrt%28x%5E2%29%2Asqrt%28x%29%2Asqrt%28y%5E2%29%2Asqrt%28y%5E2%29 Take the square root of 25 to get 5.


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


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


5x%5E2y%5E2%2Asqrt%28x%29 Rearrange and multiply.


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Answer:


So sqrt%2825%2Ax%5E5%2Ay%5E4%29 simplifies to 5x%5E2y%5E2%2Asqrt%28x%29


In other words, sqrt%2825%2Ax%5E5%2Ay%5E4%29=5x%5E2y%5E2%2Asqrt%28x%29 where every variable is positive.