simplify the following expressions?

Question

My algebrator is having a hard time with the input of these square roots

y^2 Sqrt 75yu^2 -8u Sqrt 12y^5

to draw it is so hard
_________________
(y^2) .Y (75yu^2)

there is no way to draw it

it just needs to be simplified..

Answer 1

What's an algebrator?

y^2 √(75u^2) = y^2*u*5*√3

8u √(12y^5) = y^2*u*5*√3

So their difference is:

y^2*u*5*√3 - y^2*u*5*√3 =
5uy^2√3 - 5uy^2√3 =
0

~ ♥ ~

Answer 2

If I'm reading your expression correctly, you want to simplify (using Sqrt for square root):

(y^2) Sqrt(75yu^2) - 8uSqrt(12y^5)
=Sqrt(75 y^4 y u^2) - Sqrt(768 y^5 u^2)
=Sqrt(75) Squrt(y^5 u^2) - Sqrt(768) Sqrt(y^5 u^2)
= Sqrt (y^5 u^2) {Sqrt(75) - Sqrt(768)}

You can plug the constants into a calculator if you like, I don't know if it works out to anything simple.

Hope that helps, (and that I'm reading your question right)
Matt

Answer 3

let f = y^2 Sqrt 75yu^2 -8u Sqrt 12y^5
so f^2 = y^4(75yu^2) - 64y^2(12y^5)
f^2 = 75y^4u^2 - 768y^7u
f^2 = y^4u^2(75 - 768y^3/u)
so f = y^2u(sqrt(75 - 768y^3/u))

Answer 4

sqrt (75yu^2) = 5u*sqrt(5)
sqrt(12y^5)= 2y^2*sqrt(3y)
Thus the expression becomes:
y^2*5u*sqrt(5) -8u*2y^2*sqrt(3y), or

y^2*u[5 sqrt(5) - 16*sqrt(3y)]

Answer 5

y^2Sqrt[75yu^2]-8uSqrt[12y^5]
5uy^2Sqrt[3y]-8(2)y^2Sqrt[3y]
5uy^2Sqrt[3y]-16uy^2Sqrt[3y]
(5uy^2-16uy^2)Sqrt[3y]
uy^2(5-16)Sqrt[3y]
-11uy^2Sqrt[3y]