SOLUTION: please help me simplify this problem? sqrt{{{75a^2}}}/sqrt{{{5}}}

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Question 78896: please help me simplify this problem?
sqrt75a%5E2/sqrt5
Found 4 solutions by tutor_paul, MathTherapy, timofer, ikleyn:
Answer by tutor_paul(519) About Me  (Show Source):
You can put this solution on YOUR website!
%28sqrt%2875a%5E2%29%29%2F%28sqrt%285%29%29
The first step is to recognize that sqrt%28a%5E2%29=a, so you can rewrite it as:
%28a%2Asqrt%2875%29%29%2F%28sqrt%285%29%29
Now, you need to see that 75=5%2A4%2A4, so you can also pull out a 4 from under the radical:
%284a%2Asqrt%285%29%29%2F%28sqrt%285%29%29
Finally, cancel out the sqrt%285%29 term, and you are done:
4a
Good Luck,
tutor_paul@yahoo.com

Answer by MathTherapy(10801) About Me  (Show Source):
You can put this solution on YOUR website!
please help me simplify this problem?
sqrt75a%5E2/sqrt5
*************************************
The other person wrote, "Now, you need to see that 75=5%2A4%2A4, so you can also pull out a 4 from under the radical"
How does this make sense? In what universe is 75=5%2A4%2A4? As a result, his answer, 4a is obviosly WRONG!!

highlight%28sqrt%2875a%5E2%29%2Fsqrt%285%29%29 = sqrt%2875a%5E2%2F5%29 = sqrt%2815a%5E2%29 = highlight%28matrix%281%2C4%2C+a%2Asqrt%2815%29%2C%22%2C%22%2C+or%2C+sqrt%2815%29a%29%29

Answer by timofer(155) About Me  (Show Source):
Answer by ikleyn(53742) About Me  (Show Source):
You can put this solution on YOUR website!
.
please help me simplify this problem?
sqrt%2875%2Aa%5E2%29%2Fsqrt%285%29
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~


The right way to simplify is THIS

        sqrt%2875%2Aa%5E2%29%2Fsqrt%285%29 = sqrt%2815a%5E2%29 = abs%28a%29%2Asqrt%2815%29 = sqrt%2815%29%2Aabs%28a%29.         ANSWER


                Solved completely and correctly.


According to commonly accepted agreements about square root,
the expression  ' a%5E2 '  always goes from the square root as  |a|,  the absolute value of  'a'.

In this form,  this transformation works universally for positive and negative values of  ' a '.

The given problem is a standard  TRAP  to catch  highlight%28highlight%28millions%29%29  of those,  who are unfamiliar with this trap for advance.

My post shows and teaches a standard way to avoid this trap.


As tutor @MathTherapy likes to say,  " do not accept any other answer ".