SOLUTION: Hello. I would like to get some help with a few issues I'm having if you don't mind. Been out of school for a long, long while and I need your help with: Rewriting in simplifi

Algebra ->  Real-numbers -> SOLUTION: Hello. I would like to get some help with a few issues I'm having if you don't mind. Been out of school for a long, long while and I need your help with: Rewriting in simplifi      Log On


   



Question 341827: Hello. I would like to get some help with a few issues I'm having if you don't mind. Been out of school for a long, long while and I need your help with:
Rewriting in simplified radical form sqrt()54x^4 (my answer was 3x- sqrt()6)
Simplifying u sqrt()50x^5 +6x^2 sqrt()8xu^2 (my answer was 10x + 4xu)
Simplifying sqrt() 2y^2v^3 sqrt() 10yv^4
Simplifying 10r^2s/7pq^2/5r^3s^2/21q^3 and
Add but put in lowest terms -4v+8x over 4v + 5v-4x over 4v
I greatly appreciate any help or insight you could give on these issues I'm having and I'm thanking you in advance for your assistance. :)

Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
Rewriting in simplified radical form sqrt()54x^4 (my answer was 3x- sqrt()6)
===
sqrt(54x^4) = sqrt(9x^4)*sqrt(6) = 3x^2*sqrt(6)
----------------------------------------------------------------
Simplifying u sqrt()50x^5 +6x^2 sqrt()8xu^2 (my answer was 10x + 4xu)
---
u*sqrt(50x^5)+6x^2*sqrt(8xu^2)
= 5ux^2*sqrt(2x)+6x^2*2u*sqrt(2x)
---
= (5ux^2+12ux^2)*sqrt(2x)
= (17ux^2)*sqrt(2x)
---------------------------------------
Simplifying sqrt() 2y^2v^3 sqrt() 10yv^4
---
sqrt(2y^2v^3)*sqrt(10yv^4)
---
yv*sqrt(2v)*v^2*sqrt(10y)
= 2yv^3sqrt(20vy)
= 2yv^3*2*sqrt(5vy)
= 4yv^3*sqrt(5vy)
---------------------------------------
Simplifying 10r^2s/7pq^2/5r^3s^2/21q^3
Invert the denominator and multiply:
[10r^2s/7pq^2]
---
Cancel any factor common to a numerator and a denominator:
= [2/p]
= [6q]/[prs]
================

Add but put in lowest terms -4v+8x over 4v + 5v-4x over 4v
---
= [-4v+8x+5v-4x]/(4v)
---
= [4x+v]/[4v]
=================
Cheers,
Stan H.
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