Simplifying Square Root Expressions[In-Class Version ...

Simplifying Square Root Expressions[InClass Version][Algebra 1 Honors].notebook

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Aug 266:02 PM

The examples must be copied and ready for me to check once you come to class.

Homework AssignmentThe following examples have to be copied for next class

Example 1

Example 2

Example 3

Example 4

Example 5

Example 6

Example 7

Example 8

Example 9

Example 10

Example 11

Example 12


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Jul 196:13 PM

The , (“square root of b”) means

to find a number that when multiplied

with itself the product is equal to b. In

this lesson we will use the symbol to

denote the positive square root of a

number.

“ ”

Simplifying Square Roots


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First 20 Perfect Square Integers


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Example 1

Evaluate :

SOLUTION

3


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Example 2

Evaluate :

SOLUTION

No Real Solution

Whenever there is a negative number under thesquare it is not possible to get a real number.


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Example 3

Evaluate :

SOLUTION

–3If the negative sign is NOT inside the square root just take the square root of 9, and keep the negative sign.


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Example 4

Evaluate :

SOLUTION

3


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Example 5

Evaluate :

SOLUTION

7 3 + 4


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Example 6

Evaluate :

SOLUTION

5


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Simplifying & Evaluating square roots

that are not perfect squares.

1. Rewrite the number under the radical as the product of two factors. Very important one of

the factors has to be a PERFECT SQUARE

(never use 1 as your perfect square factor).

*[If there is more than 1 perfect square factor use the largest one.]

2. Give each factor it’s own square root.

3. Simplify the square root, and rewrite the expression.


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Example 7

Evaluate :

SOLUTION

The number 12 is not a PERFECT SQUARE.

There are 3 ways that the number 12 can be written as product of two factors :

or or

For this 1st example try to simplify using each option to show why it is necessary to use a factorthat is a perfect square(excluding the number 1).


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Let's start off with the factors of :

Replace the 12 under the square root with :

Give each factor its own square root.

Simplify the square roots, if possible.

The square root of 1 can be simplified to 1. Now multiply the square root 12 and 1, the product is the square root of 12. Even though 1 is a perfect square it should not be used as a factor because you will end up with the original problem.


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Let's use the factors of :




The square root of 6 or the square root of 2 cannot be simplified without the use of a calculator. Using these factors we cannot go any further.


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Let's use the factors of :





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Example 8

Evaluate :

SOLUTION


The remainder is not zero so 144 is not a perfect square factor so now try 121.



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The remainder is zero so 25 is a perfect square factor of 150.


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Example 9

Evaluate :

SOLUTION





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The remainder is zero so 81 is a perfect square factor of 243.


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Example 10

Evaluate :

SOLUTION


The largest perfect square integer than is less than 30 is 25. Start with 25 and continue this process until a perfect square factor is found or we get to the number one.



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Jul 2011:24 AM



The remainder is not zero so 4 is not a perfect square factor and we should never use the number one. This is an example to show that not all numbers can be simplified further.


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Simplifying variable expressions under a radical.

If the exponent is EVEN divide the exponent by 2. This quotient will be the new exponent and expression will be written without a radical.

EXAMPLES


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Simplifying variable expressions under a radical.

If the exponent is ODD rewrite an equivalent expression that is the product of two powers. The first power will be raised to the original exponent minus 1 and the second power will have an exponent of 1.

EXAMPLES


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Example 11

Simplify :

SOLUTION


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Example 12

Simplify :

SOLUTION

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