SOLUTION: I do not understand simplifying radicals. Could you please explain to me how to solve these kinds of problems. I have attached a link so that you can look at the problem yourself.

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Question 226003: I do not understand simplifying radicals. Could you please explain to me how to solve these kinds of problems.
I have attached a link so that you can look at the problem yourself.
http://www.teacherweb.com/GA/EvansMiddleSchool/JWard/page_514.pdf
I need explaining on questions like 36,45,46,and 48. I have not had this kind of thing explained to me at my school yet. I don't understand how to solve these problems.
Thanks so much for your time and I am sorry these are just stupid questions! (I am just not good at things like that!!)
Found 2 solutions by edjones, josmiceli:
Answer by edjones(8007) About Me  (Show Source):
You can put this solution on YOUR website!
48)
sqrt(10)*sqrt(16)/sqrt(5)
=4sqrt(10)/sqrt(5)
=%284%2Across%28sqrt%285%29%29%2Asqrt%282%29%29%2Fcross%28sqrt%285%29%29
=4sqrt(2)
.
Ed

Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
sqrt%2849%29%2Fsqrt%284%29
You can look at these 2 radicals separately
sqrt%2849%29+=+7 and
sqrt%284%29+=+2, so
sqrt%2849%29%2Fsqrt%284%29+=+7%2F2
but, also
sqrt%2849%29%2Fsqrt%284%29+=+sqrt%2849%2F4%29
sqrt%2849%2F4%29+=+sqrt%2812.25%29
On my calculator,
sqrt%2812.25%29+=+3.5
3.5+=+7%2F2
So, both ways of solving are equivilant
also
%28sqrt%2810%29%2Asqrt%2816%29%29%2Fsqrt%285%29
sqrt%2810%29+=+3.1623
sqrt%2816%29+=+4
sqrt%285%29+=+2.2361
so,
%28sqrt%2810%29%2Asqrt%2816%29%29%2Fsqrt%285%29+=+%283.1623%2A4%29%2F2.2361
%283.1623%2A4%29%2F2.2361+=+12.6492%2F2.2361
12.6492%2F2.2361+=+5.6568
but, simplifying,
%28sqrt%2810%29%2Asqrt%2816%29%29%2Fsqrt%285%29+=+sqrt%2810%2A16%29%2Fsqrt%285%29
sqrt%2810%2A16%29%2Fsqrt%285%29+=+sqrt%28%2810%2A16%29%2F5%29
sqrt%28%2810%2A16%29%2F5%29+=+sqrt%2832%29
sqrt%2832%29+=+sqrt%2816%2A2%29
sqrt%2816%2A2%29+=+sqrt%2816%29%2Asqrt%282%29
sqrt%2816%29%2Asqrt%282%29+=+4%2Asqrt%282%29
Now, I'll see if I get the same answer before I simplified
4%2Asqrt%282%29+=+4%2A1.4142
4%2A1.4142+=+5.6568
Both methods give the same answer
I hope this helps