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#1 2007-07-19 12:50:36

grms
Member
Registered: 2007-07-19
Posts: 1

square root

How do you find the square root of

√a2??? or √a4, for  √a4 it thought maybe it was 2√a. am i wrong??

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#2 2007-07-19 13:31:01

mathsyperson
Moderator
Registered: 2005-06-22
Posts: 4,900

Re: square root

If you mean √(a x 2), usually written as √(2a), then it's already in its simplest form.
You could write it as √2√a if you wanted though.

√(4a) = 2√a, because √4 = 2.


Why did the vector cross the road?
It wanted to be normal.

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#3 2007-07-19 14:13:30

John E. Franklin
Member
Registered: 2005-08-29
Posts: 3,588

Re: square root

Also note that the one-half power is the same as a square root.
And the caret ^ sign is used at times to represent the power right after the caret.
Like 81^0.5 is 9 because 9 times 9 is 81, so the square root of 81 is 9.

Also 36^0.5 is 6 because 6 times 6 is 36, so the square root of 36 is 6.

Now if we multiply both of these together, the 6 and the 9, we get 54.
But let's do it with the square roots...
81^0.5 times 36^0.5 should also be 54.  But is it??

    81
x  36
_______
   24  06
     4  8
+  0  3
_________
     2916
So 2916 ^ 0.5, is that 54???

    54 times 54...
   
     5  4
     5  4
   x_____
   25   16
     2   0
     2   0
+_________
    2916

     Yes!!!! They are the same!!!!!!  Cool!!!
I wonder why that works, I have no idea??!!


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