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.

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.

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…

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 :

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 ?

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…

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 ?

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…

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

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

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

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…

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.

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

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

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…

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.

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

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 Factors of 20 Method # 1 : 1st – list the factors of 20

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 Factors of 20 Method # 1 : 1st – list the factors of 20 2nd – find the pair that has the biggest perfect square

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 Factors of 20 Method # 1 : 1st – list the factors of 20 2nd – find the pair that has the biggest perfect square 3rd - break up your original number into this pair under radicals

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 Factors of 20 Method # 1 : 1st – list the factors of 20 2nd – find the pair that has the biggest perfect square 3rd – break up the original number into that pair under radicals 4th – simplify the square root of the perfect square

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…

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 When your answer falls below 2 stop. 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…

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 Even though there are two that work, we want the LARGEST perfect square… When your answer falls below 2 stop. 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…

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 Break up your number into the perfect square that worked and the result… 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…

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 Reduce your perfect square… 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…

Exponents & Radicals – Rules for Radicals Square root expressions  

Exponents & Radicals – Rules for Radicals Square root expressions  

Exponents & Radicals – Rules for Radicals Square root expressions  

Exponents & Radicals – Rules for Radicals Square root expressions  

Exponents & Radicals – Rules for Radicals Square root expressions  

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

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…

Exponents & Radicals – Rules for Radicals Square root expressions EXAMPLE # 4 : For which value of x should the expression be further simplified ? a) x = 15 3 x 5 77 = 7 x 11 b) x = 21 3 x 7 c) x = 39 3 x 13 d) x = 51 3 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…

Exponents & Radicals – Rules for Radicals Square root expressions EXAMPLE # 4 : For which value of x should the expression be further simplified ? a) x = 15 3 x 5 77 = 7 x 11 b) x = 21 3 x 7 c) x = 39 3 x 13 d) x = 51 3 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 )

Exponents & Radicals – Rules for Radicals Square root expressions EXAMPLE # 4 : For which value of x should the expression be further simplified ? a) x = 15 3 x 5 77 = 7 x 11 b) x = 21 3 x 7 c) x = 39 3 x 13 d) x = 51 3 x 17 Now rewrite the expression with the factors of 77 and 21…

Exponents & Radicals – Rules for Radicals Square root expressions  

Exponents & Radicals – Rules for Radicals Square root expressions  

Exponents & Radicals – Rules for Radicals Square root expressions  

Exponents & Radicals – Rules for Radicals Square root expressions word/application problems EXAMPLE : The diagonal of a computer monitor is 160 inches long. Find the simplified form for the length of the diagonal measure.

Exponents & Radicals – Rules for Radicals Square root expressions word/application problems EXAMPLE : The diagonal of a computer monitor is 160 inches long. Find the simplified form for the length of the diagonal measure. SOLUTION : 160 = 16 ∙ 10

Exponents & Radicals – Rules for Radicals Square root expressions word/application problems EXAMPLE : The diagonal of a computer monitor is 160 inches long. Find the simplified form for the length of the diagonal measure. SOLUTION : 160 = 16 ∙ 10 160 = 4 ∙ 10

Exponents & Radicals – Rules for Radicals Square root expressions word/application problems EXAMPLE : The diagonal of a computer monitor is 160 inches long. Find the simplified form for the length of the diagonal measure. SOLUTION : 160 = 16 ∙ 10 160 = 4 ∙ 10 ANSWER : 4 10

𝐴=9𝑥 Exponents & Radicals – Rules for Radicals Square root expressions word/application problems EXAMPLE # 2 : The diagram shows a window in the shape of a square. Each side of the square measures 3 5 feet, and the area is equal to 9𝑥 square feet. Find the value of 𝑥 . 𝐴=9𝑥 3 5 ft.

𝐴=9𝑥 Exponents & Radicals – Rules for Radicals Square root expressions word/application problems EXAMPLE # 2 : The diagram shows a window in the shape of a square. Each side of the square measures 3 5 feet, and the area is equal to 9𝑥 square feet. Find the value of 𝑥 . Solution : 𝐴= 𝑠 2 𝐴=9𝑥 3 5 ft.

𝐴=9𝑥 Exponents & Radicals – Rules for Radicals Square root expressions word/application problems EXAMPLE # 2 : The diagram shows a window in the shape of a square. Each side of the square measures 3 5 feet, and the area is equal to 9𝑥 square feet. Find the value of 𝑥 . Solution : 𝐴= 𝑠 2 9𝑥= (3 5 ) 2 𝐴=9𝑥 3 5 ft.

𝐴=9𝑥 Exponents & Radicals – Rules for Radicals Square root expressions word/application problems EXAMPLE # 2 : The diagram shows a window in the shape of a square. Each side of the square measures 3 5 feet, and the area is equal to 9𝑥 square feet. Find the value of 𝑥 . Solution : 𝐴= 𝑠 2 9𝑥= (3 5 ) 2 9𝑥= (3) 2 ∙ ( 5 ) 2 9𝑥=9 ∙5 𝐴=9𝑥 3 5 ft.

𝐴=9𝑥 Exponents & Radicals – Rules for Radicals Square root expressions word/application problems EXAMPLE # 2 : The diagram shows a window in the shape of a square. Each side of the square measures 3 5 feet, and the area is equal to 9𝑥 square feet. Find the value of 𝑥 . Solution : 𝐴= 𝑠 2 9𝑥= (3 5 ) 2 9𝑥= (3) 2 ∙ ( 5 ) 2 9𝑥=9 ∙5 9𝑥=45 𝑥=5 𝐴=9𝑥 3 5 ft.