SOLUTION: Can you please help me i am doing radicals and square roots. i am having so much problems. Here are the problems: 1.)square root of 128y^4 fraction bar 64^2 2.)square root of 64

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Question 388732: Can you please help me i am doing radicals and square roots. i am having so much problems.
Here are the problems:
1.)square root of 128y^4 fraction bar 64^2
2.)square root of 64x^2, 21y^3, 72z^2
Thank you very much
Found 2 solutions by Alan3354, josmiceli:
Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
1.)square root of 128y^4 fraction bar 64^2
sqrt%28128y%5E4%2F64%5E2%29
= sqrt%282y%5E4%2F64%29
= %28y%5E2%2F8%29%2Asqrt%282%29
--------------------------
2.)square root of 64x^2
= 8x
----------
21y^3
= y*sqrt(21y)
-----------
72z^2
= 6z*sqrt(2)

Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
1)
Is the problem sqrt%28128%2Ay%5E4%2F64%5E2%29 ?
If so, think of it in a way that makes sense to you.
You should know both of these basic rules:
%28sqrt%28x%29%29%5E2+=+x
and
sqrt%28x%5E2%29+=+x
sqrt%28x%5E2%29+=+-x
Of course, x can be any positive number
Rewrite your problem to simplify it
sqrt%282%2A64%2Ay%5E4%2F64%5E2%29
Right away I see that 64%2F64%5E2+=+1%2F64, so now I have
sqrt%282%2Ay%5E4%2F64%29
This is the same as
sqrt%281%2F64%29%2Asqrt%282%2Ay%5E4%29
%281%2F8%29%2Asqrt%282%2Ay%5E2%2Ay%5E2%29
%281%2F8%29%2Asqrt%282%29%2Asqrt%28y%5E2%29%2Asqrt%28y%5E2%29
%281%2F8%29%2Asqrt%282%29%2Ay%2Ay
%281%2F8%29%2Asqrt%282%29%2Ay%5E2
This answer can actually be plus or minus. I don't know if you've
covered this yet
I'll do 1 more:
sqrt%2821y%5E3%29
There are no perfect squares contained in 21, since
the only factors are 3 and 7
sqrt%2821%29%2Asqrt%28y%5E2%29%2A+sqrt%28y%29
From the rules:
sqrt%2821%29%2Ay%2Asqrt%28y%29
This answer is NOT plus or minus because of the odd exponent in y%5E3