SOLUTION: Please Help. I'm horrible with radicals! Simplify each radical expression. Use absolute value symbols when needed. 1.) ∛-27x^6 2.) √a^4b^2 3.) 5th root√

Algebra ->  Rational-functions -> SOLUTION: Please Help. I'm horrible with radicals! Simplify each radical expression. Use absolute value symbols when needed. 1.) ∛-27x^6 2.) √a^4b^2 3.) 5th root√      Log On


   



Question 568687: Please Help. I'm horrible with radicals!
Simplify each radical expression. Use absolute value symbols when needed.
1.) ∛-27x^6
2.) √a^4b^2
3.) 5th root√-32s^15t^10
4.) ∜256y^8
5.) (2-√5)(2+√5)
6.) √48a^5b / √12ab
7.) √5(2√45-√5)
8.) 7/1-√3
9.) 5√32-7√8
10.) 2√15xy^3 x 3√30x^3y^2

Found 2 solutions by mananth, KMST:
Answer by mananth(16946) About Me  (Show Source):
You can put this solution on YOUR website!
1.) ∛-27x^6 =+-3x%5E2
2.) √a^4b^2 = a%5E2b
3.) 5th root√-32s^15t^10 = +-2s%5E3t%5E2
4.) ∜256y^8= 4y%5E2
5.) (2-√5)(2+√5)= -1
6.) √48a^5b / √12ab = 4a%5E4
7.) √5(2√45-√5)=25
8.) 7/1-√3 = %28-7%2F2%29+%2B7sqrt%283%29%2F2
9.) 5√32-7√8 = 6sqrt%282%29
10.) 2√15xy^3 x 3√30x^3y^2 = 90sqrt%282%2Ax%5E4%2Ay%5E5%29
You can find out the absolute values on a calculator

Answer by KMST(5328) About Me  (Show Source):
You can put this solution on YOUR website!
Hopefully, what I could interpret from your posting is what you meant
1) root%283%2C-27x%5E6%29
Since %28-3%29%5E3=-27 and %28x%5E2%29%5E3=x%5E%282%2A3%29=x%5E6,
root%283%2C-27x%5E6%29=root%283%2C%28-3%29%5E3%28x%5E2%29%5E3%29=root%283%2C%28-3x%5E2%29%5E3%29=-3x%5E2
2) sqrt%28a%5E4b%5E2%29=sqrt%28%28a%5E2%29%5E2%2Ab%5E2%29=sqrt%28%28a%5E2%29%5E2%29%2Asqrt%28b%5E2%29=a%5E2abs%28b%29 because sqrt%28b%5E2%29=abs%28b%29
Example:
If b=5, sqrt%285%5E2%29=sqrt%2825%29=5=b, but
if b=-5, sqrt%28%28-5%29%5E2%29=sqrt%2825%29=5=abs%28-5%29=abs%28b%29
3) root%285%2C-32s%5E15t%5E10%29
Since %28-2%29%5E5=-32, %28s%5E3%29%5E5=s%5E%283%2A5%29=s%5E15, and %28t%5E2%29%5E5=t%5E%282%2A5%29=t%5E10,
root%285%2C-32s%5E15t%5E10%29=root%285%2C%28-2%5E5%29%28s%5E3%29%5E5%28t%5E2%29%5E5%29=root%285%2C%28-2s%5E3t%5E2%29%5E5%29=-2s%5E3t%5E2
4) root%284%2C256y%5E8%29=root%284%2C2%5E8y%5E8%29=root%284%2C2%5E8%29%2Aroot%284%2Cy%5E8%29=root%284%2C%282%5E2%29%5E4%29%2Aroot%284%2C%28y%5E2%29%5E4%29=2%5E2y%5E2=4y%5E2
5) %282-sqrt%285%29%29%282%2Bsqrt%285%29%29=2%5E2-%28sqrt%285%29%29%5E2%29=4-5=-1
6)
7)
8) 7/
9)
You can simplify it further:
3sqrt%288%29=3sqrt%284%2A2%29=3%2Asqrt%284%29%2Asqrt%282%29=6%2A2sqrt%282%29=6sqrt%282%29
10)