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

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(35256) (Show Source): You can put this solution on YOUR website!
Start with the expression

First lets reduce
-----------------------------------------------------
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

Factor 108 into 36*3

Break up the square roots using the identity

Take the square root of the perfect square 36 to get 6

So the expression

simplifies to

-----------------------------------------------------

Simplify the square root (using the technique above)

Break up the fraction

Divide to get

Divide to get

So the expression

simplifies to

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

Start with the expression

First lets reduce
-----------------------------------------------------
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

Factor 20 into 4*5

Break up the square roots using the identity

Take the square root of the perfect square 4 to get 2

So the expression

simplifies to

-----------------------------------------------------

Simplify the square root (using the technique above)

Break up the fraction

Divide to get

Divide to get

So the expression

simplifies to

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