SOLUTION: i AM IN NEED OF SOME HELP WITH THESE PROBLEMS i AM NOT DOING TO WELL AT THEM -9-SQUARE 108 OVER 3 AND 6-SQAURE 20 OVER 2 tHANKS A MILLION FOR THE HELP

Algebra ->  Algebra  -> Radicals -> SOLUTION: i AM IN NEED OF SOME HELP WITH THESE PROBLEMS i AM NOT DOING TO WELL AT THEM -9-SQUARE 108 OVER 3 AND 6-SQAURE 20 OVER 2 tHANKS A MILLION FOR THE HELP      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 90237: i AM IN NEED OF SOME HELP WITH THESE PROBLEMS i AM NOT DOING TO WELL AT THEM
-9-SQUARE 108 OVER 3
AND 6-SQAURE 20 OVER 2
tHANKS A MILLION FOR THE HELP
Answer by jim_thompson5910(21667) About Me  (Show Source):
You can put this solution on YOUR website!
Start with the expression
%28-9+-+sqrt%28108%29%29%2F3

First lets reduce sqrt%28108%29
-----------------------------------------------------
sqrt%28108%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 108
Factors:
1, 2, 3, 4, 6, 9, 12, 18, 27, 36, 54,


Notice how 36 is the largest perfect square, so lets break 108 down into 36*3


sqrt%2836%2A3%29 Factor 108 into 36*3

sqrt%2836%29%2Asqrt%283%29 Break up the square roots using the identity sqrt%28x%2Ay%29=sqrt%28x%29%2Asqrt%28y%29

6%2Asqrt%283%29 Take the square root of the perfect square 36 to get 6

So the expression

sqrt%28108%29

simplifies to

6%2Asqrt%283%29
-----------------------------------------------------

%28-9+-+6%2Asqrt%283%29%29%2F3 Simplify the square root (using the technique above)

-9%2F3+-+6%2Asqrt%283%29%2F3 Break up the fraction

-3+-+6%2Asqrt%283%29%2F3 Divide -9%2F3 to get -3

-3+-+2%2Asqrt%283%29 Divide 6%2F3 to get 2



So the expression
%28-9+-+sqrt%28108%29%29%2F3

simplifies to

-3+-+2%2Asqrt%283%29


===================================================



Start with the expression
%286+-+sqrt%2820%29%29%2F2

First lets reduce sqrt%2820%29
-----------------------------------------------------
sqrt%2820%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 20
Factors:
1, 2, 4, 5, 10,


Notice how 4 is the largest perfect square, so lets break 20 down into 4*5


sqrt%284%2A5%29 Factor 20 into 4*5

sqrt%284%29%2Asqrt%285%29 Break up the square roots using the identity sqrt%28x%2Ay%29=sqrt%28x%29%2Asqrt%28y%29

2%2Asqrt%285%29 Take the square root of the perfect square 4 to get 2

So the expression

sqrt%2820%29

simplifies to

2%2Asqrt%285%29
-----------------------------------------------------

%286+-+2%2Asqrt%285%29%29%2F2 Simplify the square root (using the technique above)

6%2F2+-+2%2Asqrt%285%29%2F2 Break up the fraction

3+-+2%2Asqrt%285%29%2F2 Divide 6%2F2 to get 3

3+-+sqrt%285%29 Divide 2%2F2 to get 1



So the expression
%286+-+sqrt%2820%29%29%2F2

simplifies to

3+-+sqrt%285%29