Hello,

I am working on exercise 14 of number properties guide (roots page 67) and I am having difficulties simplifying the following :
SQRT X^2 * Y^3 + 3X^2* Y^3

when I simplify i find this result :

1) SQRT 4X^2 + 2Y^3

and i simplify to get this final result:

2) 2XY*SQRT 2Y

However the answer in the book is

2XY*SQRT Y

so it seems that the problem is with simplifying the

2Y^3

I would very much appreciate some help with understanding what I'm doing wrong here.

thanks

:idea:

You are trying to add the x's and y's individually without regard to the fact that there are two separate terms with multiplied variables. Can't do that.

Try this analogous situation:
xy + 2xy
does this equal 3x + 2y? No. The first term has one "xy" and the second term has two "xy"s so there are a total of three "xy"s
xy + 2xy = 3xy

Same thing in the problem above:
(x^2*y^3) + 3(x^2*y*3)
First, I have one of these "x^2*y^3" terms and then I have three more, so I have four total
(x^2*y^3) + 3(x^2*y*3) = 4(x^2*y*3)

Put that all under a square root sign:
pull the 4 out to get a 2
pull the x^2 out to get an x
pull a y^2 out to get a y
one y is still stuck under the square root sign

SQRT 4*x^2*y*3 = 2xySQRTy

Stacey many thanks for your help with this problem I perfectly understand my mistake now ! THANK YOU !

you're welcome!