SOLUTION: I need help simplifying radical form of 243. The inital promlem is 9SQ + bSQ= 18SQ. HELP!!!!

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Question 390396: I need help simplifying radical form of 243. The inital promlem is 9SQ + bSQ= 18SQ. HELP!!!!
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
Note: Thanks for supplying the original problem. You have the correct steps so far.


sqrt%28243%29 Start with the given expression


The goal of simplifying expressions with square roots is to factor the radicand into a product of two numbers. One of these two numbers must be a perfect square. When you take the square root of this perfect square, you will get a rational number.


So let's list the factors of 243


Factors:
1, 3, 9, 27, 81, 243


Notice how 81 is the largest perfect square, so lets factor 243 into 81*3


sqrt%2881%2A3%29 Factor 243 into 81*3


sqrt%2881%29%2Asqrt%283%29 Break up the square roots using the identity sqrt%28x%2Ay%29=sqrt%28x%29%2Asqrt%28y%29


9%2Asqrt%283%29 Take the square root of the perfect square 81 to get 9


So the expression sqrt%28243%29 simplifies to 9%2Asqrt%283%29


In other words, sqrt%28243%29=9%2Asqrt%283%29


So b=9%2Asqrt%283%29


If you need more help, email me at jim_thompson5910@hotmail.com

Also, feel free to check out my tutoring website

Jim