First you simplify the equation then you factor 184 into its prime factors which is 184 = 23 • 23
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: 4 = 22 Factors which will remain inside the root are: 46 = 2 • 23 To complete this part of the simplification we take the square root of the factors which are to be extracted. We do this by dividing their exponents by 2: 2 = 2 At the end of this step the partly simplified SQRT looks like this: 2 • sqrt (46x5y50) Rules for simplifing variables which may be raised to a power: (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 odd 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 find out that SQRT(x5y50) = x2y25 • SQRT(x) sqrt (184x5y50) = 2 x2y25 • sqrt(46x)
