SOLUTION: What is 18 + the square root of 567 over 9 equal?

Algebra ->  Radicals -> SOLUTION: What is 18 + the square root of 567 over 9 equal?      Log On


   

Question 86162: What is 18 + the square root of 567 over 9 equal?
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
%2818%2Bsqrt%28567%29%29%2F9

First lets reduce sqrt%28567%29
-------------------------------------------------------------------------
sqrt%28567%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. This way the perfect square will become a rational number.
So let's list the factors of 567
Factors:
1, 3, 7, 9, 21, 27, 63, 81, 189,


Notice how 81 is the largest perfect square, so lets break 567 down into 81*7


sqrt%2881%2A7%29 Factor 567 into 81*7

sqrt%2881%29%2Asqrt%287%29 Break up the square roots using the identity sqrt%28x%2Ay%29=sqrt%28x%29%2Asqrt%28y%29

9%2Asqrt%287%29 Take the square root of the perfect square 81 to get 9

So the expression

sqrt%28567%29

simplifies to

9%2Asqrt%287%29
-------------------------------------------------------------------------

%2818%2B9%2Asqrt%287%29%29%2F9 Simplify the square root (using the technique above)

18%2F9%2B%289%2Asqrt%287%29%29%2F9 Break up the fraction

2%2B%289%2Asqrt%287%29%29%2F9 Divide 18%2F9 to get 2

2%2B1%2Asqrt%287%29 Divide 9%2F9 to get 1

So the expression

%2818%2Bsqrt%28567%29%29%2F9

Simplifies to

2%2Bsqrt%287%29