Answer:
6xy^2
Explanation:
Changes made to your input should not affect the solution:
(1): "y4" was superseded by "y^4". 1 more homogeneous supersession(s).
Simplify :
sqrt(36x2y4)
STEP
1:
Simplify the Integer part of the SQRT
Factor 36 into its prime factors
36 = 22 • 32
To simplify a square root, we extract factors which are squares, i.e., factors that are raised to an even exponent.
Factors which will be extracted are :
36 = 22 • 32
No factors remain inside the root !!
To consummate this component of the simplification we take the squre root of the factors which are to be extracted. We do this by dividing their exponents by 2 :
6 = 2 • 3
At the cessation of this step the partly simplified SQRT looks akin to this:
6 sqrt(x2y4)
STEP
2
:
Simplify the Variable part of the SQRT
Rules for simplifing variables which may be raised to a potency:
(1) variables with no exponent stay inside the radical
(2) variables raised to power 1 or (-1) stay inside the radical
(3) variables raised to an even exponent: Half the exponent taken out, nothing remains inside the radical. examples:
(3.1) sqrt(x8)=x4
(3.2) sqrt(x-6)=x-3
(4) variables raised to an eccentric exponent which is >2 or <(-2) , examples:
(4.1) sqrt(x5)=x2•sqrt(x)
(4.2) sqrt(x-7)=x-3•sqrt(x-1)
Applying these rules to our case we ascertain that
SQRT(x2y4) = xy2
Coalesce both simplifications
sqrt (36x2y4) =
6 xy2