SOLUTION: This is from a worksheet. I have 2 questions that i'm not sure on. Direction say simplify. Assume that no denominator equals 0. 1. sq. root 16x^2y^4 2. sq root 12-sq root 18

Algebra ->  Algebra  -> Radicals -> SOLUTION: This is from a worksheet. I have 2 questions that i'm not sure on. Direction say simplify. Assume that no denominator equals 0. 1. sq. root 16x^2y^4 2. sq root 12-sq root 18      Log On

Ad: Algebrator™ solves your algebra problems and provides step-by-step explanations!
Ad: Algebra Solved!™: algebra software solves algebra homework problems with step-by-step help!

   

Question 162013: This is from a worksheet. I have 2 questions that i'm not sure on.
Direction say simplify. Assume that no denominator equals 0.
1. sq. root 16x^2y^4
2. sq root 12-sq root 18+3sq root 50+sq root 75.
Sorry i don't have a sq. root sign on my computer
Please. help
Thanks

Answer by jim_thompson5910(21667) About Me  (Show Source):
You can put this solution on YOUR website!
1)

For these type of problems, it is crucial to remember that sqrt%28x%5E2%29=x where x%3E=0 (ie it's not negative)

sqrt%2816x%5E2y%5E4%29 Start with the given expression


sqrt%284%5E2%2Ax%5E2y%5E4%29 Rewrite 16 as 4%5E2


sqrt%284%5E2%2Ax%5E2%28y%5E2%29%5E2%29 Rewrite y%5E4 as %28y%5E2%29%5E2


sqrt%284%5E2%29%2Asqrt%28x%5E2%29%2Asqrt%28%28y%5E2%29%5E2%29 Break up the square root.


4xy%5E2 Use the formula above to simplify each square root. So in this case sqrt%284%5E2%29=4, sqrt%28x%5E2%29=x, and sqrt%28%28y%5E2%29%5E2%29=y%5E2


So sqrt%2816x%5E2y%5E4%29=4xy%5E2 every variable is nonnegative





2)

sqrt%2812%29-sqrt%2818%29%2B3%2Asqrt%2850%29%2Bsqrt%2875%29 Start with the given expression

Now we must factor each number in the square roots into two number where one MUST be a perfect square.

sqrt%284%2A3%29-sqrt%289%2A2%29%2B3%2Asqrt%2825%2A2%29%2Bsqrt%2825%2A3%29 Factor 12 into 4%2A3. Factor 18 into 9%2A2. Factor 50 into 25%2A2. Factor 75 into 25%2A3.


sqrt%284%29%2Asqrt%283%29-sqrt%289%29%2Asqrt%282%29%2B3%2Asqrt%2825%29%2Asqrt%282%29%2Bsqrt%2825%29%2Asqrt%283%29 Break p the square roots


sqrt%282%5E2%29%2Asqrt%283%29-sqrt%283%5E2%29%2Asqrt%282%29%2B3%2Asqrt%285%5E2%29%2Asqrt%282%29%2Bsqrt%285%5E2%29%2Asqrt%283%29 Rewrite 4 as 2%5E2. Rewrite 9 as 3%5E2. Rewrite 25 as 5%5E2

2%2Asqrt%283%29-3%2Asqrt%282%29%2B3%2A5%2Asqrt%282%29%2B5%2Asqrt%283%29 Take the square root of the perfect squares to simplify the square roots. So sqrt%282%5E2%29=2, sqrt%283%5E2%29=3, and sqrt%285%5E2%29=5


2%2Asqrt%283%29-3%2Asqrt%282%29%2B15%2Asqrt%282%29%2B5%2Asqrt%283%29 Multiply


%28-3%2Asqrt%282%29%2B15%2Asqrt%282%29%29%2B%282%2Asqrt%283%29%2B5%2Asqrt%283%29%29 Group the common terms.


12%2Asqrt%282%29%2B7%2Asqrt%283%29 Combine the common terms.


So sqrt%2812%29-sqrt%2818%29%2B3%2Asqrt%2850%29%2Bsqrt%2875%29=12%2Asqrt%282%29%2B7%2Asqrt%283%29