SOLUTION: Simplify by factoring the square root of 1575x^4 (x is to the 4th power). I don't know how to find the largest perfect square factor of a number, especially bigger numbers. I co

Algebra ->  Square-cubic-other-roots -> SOLUTION: Simplify by factoring the square root of 1575x^4 (x is to the 4th power). I don't know how to find the largest perfect square factor of a number, especially bigger numbers. I co      Log On


   

Question 325222: Simplify by factoring the square root of 1575x^4 (x is to the 4th power). I don't know how to find the largest perfect square factor of a number, especially bigger numbers.
I couldn't view the dropdown option for the topic of my question, I appologize.
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
sqrt%281575%2Ax%5E4%29 Start with the given expression.


sqrt%28225%2A7%2Ax%5E4%29 Factor 1575 into 225%2A7


sqrt%28225%2A7%2Ax%5E2%2Ax%5E2%29 Factor x%5E4 into x%5E2%2Ax%5E2


sqrt%28225%29%2Asqrt%287%29%2Asqrt%28x%5E2%29%2Asqrt%28x%5E2%29 Break up the square root using the identity sqrt%28A%2AB%29=sqrt%28A%29%2Asqrt%28B%29.


15%2Asqrt%287%29%2Asqrt%28x%5E2%29%2Asqrt%28x%5E2%29 Take the square root of 225 to get 15.


15%2Asqrt%287%29%2Ax%2Ax Take the square root of x%5E2 to get x.


15x%5E2%2Asqrt%287%29 Rearrange and multiply the terms.

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Answer:


So sqrt%281575%2Ax%5E4%29 simplifies to 15x%5E2%2Asqrt%287%29


In other words, sqrt%281575%2Ax%5E4%29=15x%5E2%2Asqrt%287%29 where x%3E=0