SOLUTION: Can somebody Please help me solve this problem? I have been working on it a long time and I still do not understand it. Simplify as much as possible x sqrt 6t^3-tsqrt24tx^2

Algebra ->  Quadratic Equations and Parabolas  -> Quadratic Equations Lessons -> SOLUTION: Can somebody Please help me solve this problem? I have been working on it a long time and I still do not understand it. Simplify as much as possible x sqrt 6t^3-tsqrt24tx^2       Log On


   

Question 322848: Can somebody Please help me solve this problem? I have been working on it a long time and I still do not understand it.
Simplify as much as possible
x sqrt 6t^3-tsqrt24tx^2
Assume that all variables represent positive real numbers
Found 4 solutions by stanbon, jim_thompson5910, Earlsdon, rapaljer:
Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
Simplify as much as possible:

(x sqrt(6t^3) - (tsqrt(24tx^2))
------
= x*t*sqrt(6t) - t*2xsqrt(6t)
---
= (xt*sqrt(6t)(1 - 2)
---
= -xtsqrt(6t)
=====================
Cheers,
Stan H.

Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
x%2Asqrt%286t%5E3%29-t%2Asqrt%2824tx%5E2%29 Start with the given expression.


x%2Asqrt%286t%5E2%2At%29-t%2Asqrt%2824tx%5E2%29 Factor t%5E3 into t%5E2%2At


x%2Asqrt%286t%5E2%2At%29-t%2Asqrt%284%2A6tx%5E2%29 Factor 24tx%5E2 into 4%2A6tx%5E2


Break up the roots.


Take the square root of 4 to get 2


x%2Asqrt%286%29%2At%2Asqrt%28t%29-t%2A2%2Asqrt%286%29%2Asqrt%28t%29%2Asqrt%28x%5E2%29 Take the square root of t%5E2 to get 't'


x%2Asqrt%286%29%2At%2Asqrt%28t%29-t%2A2%2Asqrt%286%29%2Asqrt%28t%29%2Ax Take the square root of x%5E2 to get 'x'


tx%2Asqrt%286t%29-2tx%2Asqrt%286t%29 Rearrange the terms and combine the roots.


sqrt%286t%29%28tx-2tx%29 Factor out sqrt%286t%29


sqrt%286t%29%28-tx%29 Combine like terms.


-tx%2Asqrt%286t%29 Rearrange the terms.


So x%2Asqrt%286t%5E3%29-t%2Asqrt%2824tx%5E2%29=-tx%2Asqrt%286t%29

Answer by Earlsdon(6294) About Me  (Show Source):
You can put this solution on YOUR website!
Simplify:
x%2Asqrt%286t%5E3%29-t%2Asqrt%2824tx%5E2%29 Rewrite this as:
x%2Asqrt%286t%2At%5E2%29-t%2Asqrt%284%2Ax%5E2%2A6t%29 Now take the square root of the perfect squares that are under the radical and move them outside.
x%2At%2Asqrt%286t%29-2xt%2Asqrt%286t%29 Factor the common factor of sqrt%286t%29.
%28sqrt%286t%29%29%2A%28xt-2xt%29 Perform the indicated subtraction.
%28sqrt%286t%29%29%2A%28-xt%29 or highlight%28-xt%2Asqrt%286t%29%29

Answer by rapaljer(4671) About Me  (Show Source):
You can put this solution on YOUR website!
x%2Asqrt%286t%5E3%29-t%2Asqrt%2824tx%5E2%29
x%2Asqrt%28t%5E2%29%2Asqrt%286t%29-t%2Asqrt%284x%5E2%29%2Asqrt%286t%29
x%2At%2Asqrt%286t%29-t%2A2x%2Asqrt%286t%29
1xt%2Asqrt%286t%29-2xt%2Asqrt%286t%29
-xt%2Asqrt%286t%29

For additional help with square roots, please see my own website. Click on my tutor name "rapaljer" anywhere in algebra.com. There, click on my website. From my Homepage, look for the link near the top of the page "Basic, Intermediate, and College Algebra: One Step at a Time." Then click on "Basic Algebra", then "Chapter 5", "Sections 5.01, 5.03, and 5.04." There you will find my own non-traditional explanations, examples, exercises, and answers to ALL the exercises, and solutions to many of the problems on the "MATH IN LIVING COLOR" pages that go with these explanations.

For an explanation of this topic at a slightly higher level, look in the "Basic, Intermediate, and College Algebra: One Step at a Time" topic for "Intermediate Algebra." Radicals are in "Chapter 3", sections 3.01 and 3.02 for Intermediate Algebra.

See also the FREE video from my own classes a few years before I retired! From my Homepage, look for the link "Rapalje Videos in Living Color". Then look for "Basic Algebra", and choose the "Radicals" link. You may need to download RealPlayer if you do not have it, but this is a FREE download. Like algebra.com, this is all FREE!!

Dr. Robert J. Rapalje, Retired
Seminole State College of Florida
Altamonte Springs Campus