SOLUTION: Hello. I really don't understand the whole simplifying radicals thing I learned today in class. I was wondering is you could explain it to me because my classmates couldn't help me

Question 60039: Hello. I really don't understand the whole simplifying radicals thing I learned today in class. I was wondering is you could explain it to me because my classmates couldn't help me.

The directions say to express each radical in simplest form.

under the radical sign it says 75x12(to the twelfth)y5(to the fifth).

one of the other ones says

4 as the index, then under the radical sign 48x3(to the third)y20(to the twentith)

if anyone could help me it would me greatly appreciated.Thanks.
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
under the radical sign it says 75x12(to the twelfth)y5(to the fifth).
Rewrite the radicand: Separate it into two factors, one of which is a
perfect square, as follows:
=sqrt[(25*x^12y^4)(3y)]
Take the square root of the perfect square factor, as follows:
=5*x^6*y^2 sqrt(3y)
--------------------
one of the other ones says
4 as the index, then under the radical sign 48x3(to the third)y20(to the twentith)
4th root of (48x^3y^20)
Separate the radicand into two factors, one of which is a perfect 4th power.
=4th root of [(16y^20))(3x^3)]
Take the 4th root of the pervect 4th power factor to get:
=2y^5[4th root of (3x^3)]
---------
Cheers,
Stan H.

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