SOLUTION: I need help with this problem. My math teacher goes very fast and I sometimes have a hard time keeping up. I do not know how to get the same number under the radical. I dont kno

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Question 123482This question is from textbook Algebra 2
: I need help with this problem. My math teacher goes very fast and I sometimes have a hard time keeping up. I do not know how to get the same number under the radical. I dont know how to make 1250 and 32 the same so that I can subtract 8 from 2. THANK YOU This question is from textbook Algebra 2

Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
I need help with this problem. My math teacher goes very fast and I sometimes have a hard time keeping up. I do not know how to get the same number under the radical. I dont know how to make 1250 and 32 the same so that I can subtract 8 from 2.
:
I'm not sure what you mean here, assuming:
sqrt%281250%29+-+sqrt%2832%29 =
:
Factor as much as we can here
sqrt%282%2A5%2A5%2A5%2A5%29+-+sqrt%282%2A2%2A2%2A2%2A2%29 =
:
Use this to see how many square we have in there
sqrt%282%2A25%2A25%29+-+sqrt%282%2A4%2A4%29 =
:
Factor out the square roots of the perfect squares:
5%2A5%2Asqrt%282%29+-+2%2A2%2Asqrt%282%29 =
which is
25%2Asqrt%282%29+-+4%2Asqrt%282%29 =
:
Now they are like terms so we an just subtract 4 from 25 and we have
21%2ASqrt%282%29
;
:
We can check this on good calc like this
1st enter the original problem: sqrt%281250%29+-+sqrt%2832%29 = 29.698..
then
Enter our solution: 21%2Asqrt%282%29 = 29.698.. also; proves our solution
:
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