SOLUTION: simplify: 4√400/ 4√5. Show your work(i need to know how to work this problem out.

Algebra ->  Square-cubic-other-roots -> SOLUTION: simplify: 4√400/ 4√5. Show your work(i need to know how to work this problem out.      Log On


   

Question 1022235: simplify: 4√400/ 4√5. Show your work(i need to know how to work this problem out.
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
If the problem is %284%2Asqrt%28400%29%29%2F%284%2Asqrt%285%29%29, then...

StepExpression
1.%284%2Asqrt%28400%29%29%2F%284%2Asqrt%285%29%29
2.%28highlight%284%29%2Asqrt%28400%29%29%2F%28highlight%284%29%2Asqrt%285%29%29
3.%28cross%284%29%2Asqrt%28400%29%29%2F%28cross%284%29%2Asqrt%285%29%29
4.%28sqrt%28400%29%29%2F%28sqrt%285%29%29
5.sqrt%28400%2F5%29
6.sqrt%2880%29
7.sqrt%2816%2A5%29
8.sqrt%2816%29%2Asqrt%285%29
9.4%2Asqrt%285%29


So in the end, the expression simplifies to 4%2Asqrt%285%29

In other words, %284%2Asqrt%28400%29%29%2F%284%2Asqrt%285%29%29=4%2Asqrt%285%29

Final Answer: 4%2Asqrt%285%29



Notes:

* In step 5, I used the property %28sqrt%28x%29%29%2F%28sqrt%28y%29%29+=+sqrt%28x%2Fy%29

* Once I get to step 6, everything after this step is simplifying the radical. To do this, we factor 80 into 16*5 (step 7). Notice how 16 is the largest perfect square factor of 80

* In step 8, I then used sqrt%28x%29%2Asqrt%28y%29+=+sqrt%28x%2Ay%29

* As you can see in step 9, the square root of 16 is 4 which is a whole number. This is why 80 was factored into 16*5

* Keep in mind this answer only applies if my assumption at the top is true. The assumption that the problem was %284%2Asqrt%28400%29%29%2F%284%2Asqrt%285%29%29. If the assumption at the top is not true, then maybe the next assumption is true.

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OR

If the problem is %28root%284%2C400%29%29%2F%28root%284%2C5%29%29, then...


StepExpression
1.%28root%284%2C400%29%29%2F%28root%284%2C5%29%29
2.root%284%2C400%2F5%29
3.root%284%2C80%29
4.root%284%2C16%2A5%29
5.root%284%2C16%29%2Aroot%284%2C5%29
6.2%2Aroot%284%2C5%29



Final Answer: 2%2Aroot%284%2C5%29



Notes:

* For step 2, I used the property %28root%28n%2Cx%29%29%2F%28root%28n%2Cy%29%29+=+root%28n%2Cx%2Fy%29

* For step 5, I used the property root%28n%2Cx%29%2Aroot%28n%2Cy%29+=+root%28n%2Cx%2Ay%29

* Like before, to simplify the fourth root of 80, I factored 80 into 16*5 because 16 is a perfect fourth root number. Taking the fourth root of 16 yields 2 (seen on step 6)

* Keep in mind this answer only applies if my assumption at the top is true. The assumption that the problem was %28root%284%2C400%29%29%2F%28root%284%2C5%29%29. If the second assumption isn't true, then go back to the first assumption (hopefully it's true. If not, then let me know)