SOLUTION: Simplify by factoring. Assume that all expressions under radical represent nonnegative numbers. sqrt( 18a^2b ) I'm confused as I've seen similar problems set up stating to t

Algebra ->  Radicals -> SOLUTION: Simplify by factoring. Assume that all expressions under radical represent nonnegative numbers. sqrt( 18a^2b ) I'm confused as I've seen similar problems set up stating to t      Log On


   

Question 132991: Simplify by factoring. Assume that all expressions under radical represent nonnegative numbers.
sqrt( 18a^2b )
I'm confused as I've seen similar problems set up stating to think of them as positive numbers. Please help.
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
sqrt%2818a%5E2b%29 Start with the given expression


sqrt%2818%29sqrt%28a%5E2%29sqrt%28b%29 Break up the root


3%2Asqrt%282%29%2Asqrt%28a%5E2%29sqrt%28b%29%29 Simplify sqrt%2818%29 to get 3%2Asqrt%282%29


3%2Asqrt%282%29%2Aa%2Asqrt%28b%29 Simplify sqrt%28a%5E2%29 to get a


3%2Aa%2Asqrt%282b%29 Combine the square roots



So sqrt%2818a%5E2b%29 simplifies to 3%2Aa%2Asqrt%282b%29


In other words, sqrt%2818a%5E2b%29=3%2Aa%2Asqrt%282b%29 if a and b are positive numbers (since you cannot take the square root of a negative number)