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Exponents & Radicals – Rules for Radicals A radical is simply a root. The root taken is also referred to as an index. If you have a square root the index is two. If you have a cube root the index is three.

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Exponents & Radicals – Rules for Radicals A radical is simply a root. The root taken is also referred to as an index. If you have a square root the index is two. If you have a cube root the index is three. For now we will work only with square roots.

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Exponents & Radicals – Rules for Radicals A radical is simply a root. The root taken is also referred to as an index. If you have a square root the index is two. If you have a cube root the index is three. For now we will work only with square roots. Perfect Squares – numbers that are gotten by multiplying the SAME number by itself. You could create a table of perfect squares…

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Exponents & Radicals – Rules for Radicals Perfect Squares – numbers that are gotten by multiplying the SAME number by itself. You could create a table of perfect squares… To find a perfect square root, we will think of the perfect square table. Realize that table keeps going, I only went up to 12…. EXAMPLE :

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Exponents & Radicals – Rules for Radicals Perfect Squares – numbers that are gotten by multiplying the SAME number by itself. You could create a table of perfect squares… To find a perfect square root, we will think of the perfect square table. realize that table keeps going, I only went up to 12…. EXAMPLE : What number did I multiply to get 25 ?

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Exponents & Radicals – Rules for Radicals Perfect Squares – numbers that are gotten by multiplying the SAME number by itself. You could create a table of perfect squares… To find a perfect square root, we will think of the perfect square table. realize that table keeps going, I only went up to 12…. EXAMPLE : Notice there is no longer a radical over the answer…

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Exponents & Radicals – Rules for Radicals Perfect Squares – numbers that are gotten by multiplying the SAME number by itself. You could create a table of perfect squares… To find a perfect square root, we will think of the perfect square table. realize that table keeps going, I only went up to 12…. EXAMPLE : What number did I multiply to get 100 ?

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Exponents & Radicals – Rules for Radicals Perfect Squares – numbers that are gotten by multiplying the SAME number by itself. You could create a table of perfect squares… To find a perfect square root, we will think of the perfect square table. realize that table keeps going, I only went up to 12…. EXAMPLE : Notice there is no longer a radical over the answer…

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Exponents & Radicals – Rules for Radicals So now we could create a square root table…

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Exponents & Radicals – Rules for Radicals Some rules for radicals : 1. A number / variable, divided by its square root, equals its square root

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Exponents & Radicals – Rules for Radicals Some rules for radicals : 1. A number / variable, divided by its square root, equals its square root 2. Numbers / variables under THE SAME root / index can be multiplied or divided

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Exponents & Radicals – Rules for Radicals Some rules for radicals : 1. A number / variable, divided by its square root, equals its square root 2. Numbers / variables under THE SAME root / index can be multiplied or divided This rule also works in the OTHER direction, and is sometimes used to help simplify radicals…

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Exponents & Radicals – Rules for Radicals Some rules for radicals : 3. Radicals act like variables. They can be added / subtracted as long as the root / index is the same AND what is under the radical is exactly the same.

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Exponents & Radicals – Rules for Radicals Some rules for radicals : 3. Radicals act like variables. They can be added / subtracted as long as the root / index is the same AND what is under the radical is exactly the same. Just like

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Exponents & Radicals – Rules for Radicals Some rules for radicals : 3. Radicals act like variables. They can be added / subtracted as long as the root / index is the same AND what is under the radical is exactly the same. Just like

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Exponents & Radicals – Rules for Radicals Some rules for radicals : 3. Radicals act like variables. They can be added / subtracted as long as the root / index is the same AND what is under the radical is exactly the same. Just like You CAN NOT combine these. The number under the root is NOT the same…

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Exponents & Radicals – Rules for Radicals Simplifying radicals – sometimes a number under a radical can be broken into a perfect square part and a radical part.

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Exponents & Radicals – Rules for Radicals Simplifying radicals – sometimes a number under a radical can be broken into a perfect square part and a radical part. EXAMPLE # 1 : Simplify

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Exponents & Radicals – Rules for Radicals Simplifying radicals – sometimes a number under a radical can be broken into a perfect square part and a radical part. EXAMPLE # 1 : SimplifyFactors of 20 Method # 1 : 1 st – list the factors of 20

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Exponents & Radicals – Rules for Radicals Simplifying radicals – sometimes a number under a radical can be broken into a perfect square part and a radical part. EXAMPLE # 1 : SimplifyFactors of 20 Method # 1 : 1 st – list the factors of 20 2 nd – find the pair that has the biggest perfect square

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Exponents & Radicals – Rules for Radicals Simplifying radicals – sometimes a number under a radical can be broken into a perfect square part and a radical part. EXAMPLE # 1 : SimplifyFactors of 20 Method # 1 : 1 st – list the factors of 20 2 nd – find the pair that has the biggest perfect square 3 rd - break up your original number into this pair under radicals

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Exponents & Radicals – Rules for Radicals Simplifying radicals – sometimes a number under a radical can be broken into a perfect square part and a radical part. EXAMPLE # 1 : SimplifyFactors of 20 Method # 1 : 1 st – list the factors of 20 2 nd – find the pair that has the biggest perfect square 3 rd – break up the original number into that pair under radicals 4 th – simplify the square root of the perfect square

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Exponents & Radicals – Rules for Radicals Simplifying radicals – sometimes a number under a radical can be broken into a perfect square part and a radical part. EXAMPLE # 2 : Simplify Method # 2 : Go thru the perfect square table and find the LARGEST perfect square that divides your number without a remainder. We never use 1…

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Exponents & Radicals – Rules for Radicals Simplifying radicals – sometimes a number under a radical can be broken into a perfect square part and a radical part. EXAMPLE # 2 : Simplify Method # 2 : Go thru the perfect square table and find the LARGEST perfect square that divides your number without a remainder. We never use 1… When your answer falls below 2 stop.

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Exponents & Radicals – Rules for Radicals Simplifying radicals – sometimes a number under a radical can be broken into a perfect square part and a radical part. EXAMPLE # 2 : Simplify Method # 2 : Go thru the perfect square table and find the LARGEST perfect square that divides your number without a remainder. We never use 1… When your answer falls below 2 stop. Even though there are two that work, we want the LARGEST perfect square…

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Exponents & Radicals – Rules for Radicals Simplifying radicals – sometimes a number under a radical can be broken into a perfect square part and a radical part. EXAMPLE # 2 : Simplify Method # 2 : Go thru the perfect square table and find the LARGEST perfect square that divides your number without a remainder. We never use 1… Break up your number into the perfect square that worked and the result…

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Exponents & Radicals – Rules for Radicals Simplifying radicals – sometimes a number under a radical can be broken into a perfect square part and a radical part. EXAMPLE # 2 : Simplify Method # 2 : Go thru the perfect square table and find the LARGEST perfect square that divides your number without a remainder. We never use 1… Reduce your perfect square…

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Exponents & Radicals – Rules for Radicals Square root expressions

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Exponents & Radicals – Rules for Radicals Square root expressions

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Exponents & Radicals – Rules for Radicals Square root expressions

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Exponents & Radicals – Rules for Radicals Square root expressions

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Exponents & Radicals – Rules for Radicals Square root expressions

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Exponents & Radicals – Rules for Radicals Square root expressions EXAMPLE # 4 : For which value of x should the expression be further simplified ? a) x = 15 b) x = 21 c) x = 39 d) x = 51

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Exponents & Radicals – Rules for Radicals Square root expressions EXAMPLE # 4 : For which value of x should the expression be further simplified ? a) x = 15 b) x = 21 c) x = 39 d) x = 51 To solve this, we need to write down the factors of the given numbers and find a match with the factors of the number in the expression…

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Exponents & Radicals – Rules for Radicals Square root expressions EXAMPLE # 4 : For which value of x should the expression be further simplified ? a) x = 153 x 577 = 7 x 11 b) x = 213 x 7 c) x = 393 x 13 d) x = 513 x 17 To solve this, we need to write down the factors of the given numbers and find a match with the factors of the number in the expression…

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Exponents & Radicals – Rules for Radicals Square root expressions EXAMPLE # 4 : For which value of x should the expression be further simplified ? a) x = 153 x 577 = 7 x 11 b) x = 213 x 7 c) x = 393 x 13 d) x = 513 x 17 To solve this, we need to write down the factors of the given numbers and find a match with the factors of the number in the expression… As you can see, there is a match between 77 and 21 ( the factor 7 )

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Exponents & Radicals – Rules for Radicals Square root expressions EXAMPLE # 4 : For which value of x should the expression be further simplified ? a) x = 153 x 577 = 7 x 11 b) x = 213 x 7 c) x = 393 x 13 d) x = 513 x 17 Now rewrite the expression with the factors of 77 and 21…

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Exponents & Radicals – Rules for Radicals Square root expressions

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Exponents & Radicals – Rules for Radicals Square root expressions

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Exponents & Radicals – Rules for Radicals Square root expressions

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