How do you solve square root problems that have fractions with variables and exponets?

Question

i need major help. Its a fraction that has variable ( 3b^2/27b^4) square rooted

Answer 1

SQRT(3b^2/27b^4) = SQRT(1/9b^2) by straightforward algebra

 

The SQRT(A/B) = SQRT(A)/SQRT(B), so

 

SQRT(1/9b^2) = SQRT(1)/SQRT(9b^2)

 

= 1/3b

Answer 2

I think you mean √(3b²)/(27b⁴)

 

in this case, the 3 and 27 reduce to a 9 in the denominator.  The b²/b⁴ reduces down to b² in the denominator.  so you now have √(1/(9b²).  This is a perfect square so you get ± 1/(3b).  The plus or minus is necessary from the square root.

Answer 3

I assume if it is an equation, it should be set equal to some other expression? What you'd do is square both sides, because that gets you rid of the square root.

a simple example

 

sqrt(x^4)=4

therefore

 

x^4=16 (after raising both sides to the second power)