SOLUTION: Divide. Rationalize the denominator if necessary. Then simplify each radical expression. 1) 18+ square root of 567 OVER 9 2) -9- square root of 108 OVER 3 3) 6- square roo

Question 118065: Divide. Rationalize the denominator if necessary. Then simplify each radical expression.
1) 18+ square root of 567 OVER 9
2) -9- square root of 108 OVER 3
3) 6- square root of 20 OVER 2
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
I'll do the first two to show you how to do these

#1

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 567
Factors:
1, 3, 7, 9, 21, 27, 63, 81, 189, 567

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

Factor 567 into 81*7

Break up the square roots using the identity

Take the square root of the perfect square 81 to get 9

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

#2

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, 108

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

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