Question 89271: Please help. I'm really confused --I'm trying to simplify these radicals, but I'm lost as to what steps to take. My instructor gives a different method then I learned (I din't even have that down. We have a test and I don't think I'll pass this section unless I get some help.
I'm not sure how to key the radical sign on my computor keyboard. Here's a few of the problems (sorry there's more than one, but I need to know the formulas, because I notice that not all problems can be solved just the same way, so here's one of every kind of problem I'm simplifying:
The square root of 27x^3y^5
The cubed root 125x^9y^5/8x^3z^12
1/the square root of 5xy^2
2x/the 4th root of 3xy^2
x/3- the square root of x
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! The square root of 27x^3y^5
= [sqrt(9x^2y^4)[sqrt(3xy)]
= [3xy^2][sqrt(3xy)]
--------------------------
The cubed root 125x^9y^5/8x^3z^12
= cbrt[(125/8)x^6y^3 / z^12]*cbrt[y^2]
=[(5/2)x^2y/z^4]*cbrt(y^2)
--------------------------
1/the square root of 5xy^2
Multiply numerator and denominator by sqrt(5x) to get:
[sqrt(5x)] / [5xy]
---------------
2x/the 4th root of 3xy^2
Multiply numerator and denominator by 4th root of (3^3x^3y^2) to get:
[2x*4th rt of (27x^3y^2)] / [3xy]
Cancel the common factor of "x" to get:
(2/3)[4th rt of (27x^3y^2)]/[3y]
=============
x/[3- sqrt(x)]
Multiply numerator and denominator by (3+sqr(x)) to get:
[x(3+sqrtx]/[9-x]
================
Cheers,
Stan H.
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