Math-2 Lesson 2-4. Radicals

Transcription

1 Math- Lesson - Radicals

2 = What number is equivalent to the square root of? Square both sides of the equation ( ) ( ) = = = is an equivalent statement to = There is no equivalent number The decimal, is just an approimation.

3 Radicals Inde number Radical symbol Radicand = = = = = = The square root of means: what number squared equals? The rd root of means: what number cubed equals? The th root of means: what number used as a factor times equals?

4 Adding and subtracting radicals Can these two terms be combined using addition? Write as repeated addition Write as repeated addition + When multiplication is written as repeated addition, like terms look eactly alike

5 Define like powers + Define like radicals + Same base, same eponent. Same radicand, same inde number. Which of the following are like radicals that can be added?

6 + + = Are they equivalent? a + b a + b This is NOT a property of radicals. NEVER DO THIS!!!!

7 Simplify the following: not like terms in their present form 7

8 Will this work? Product of Radicals Property a b a b = Are these equivalent? a b = ab = Although I only gave two eamples, it actually DOES WORK for whole number radicand. 8

9 a b = ab Simplify the following: =

10 Simplify radicals: use the Product of Radicals to break apart the radical into a perfect square times a number. a b = ab 18 Simplify y 8 7y 7y 1y

11 Stop Here

12 Can we add unlike radicals?. a b = ab Simplify 7 + ( 7 + ) 7 + ( ) ( 1 ) + ( ) + ( ) ( ) 1 + 8

13 Simplify radicals: use the Product of Radicals to break apart the radical into a powers of eponent m times a number. Simplify y m m a b = m ab 1 8 y y y y y y y y y

14 Another way to Simplify Radicals 7 9 Factor, factor, factor!!! What is the factor that is used times under the radical? Bring that out factor (that is used times). Using Properties of Eponents to reduce the writing: 1

15 Factor the numerator! 1 Inverse Property of Multiplication Inverse Property of Multiplication y 8y 7 8y 8y Inverse Property of Multiplication 7 7 1

16 Simplify 9 0y y

17 Rationalizing the denominator: using mathematical properties to change an irrational number (or imaginary) in the denominator into a rational number. We take advantage of the idea: = = = = 9 = 1 Identity Property of Multiplication = multiplying by 1 doesn t change the number.

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19 In all of the previous eamples we just multiplied by one in the form of the denominator radical over the denominator radical It is always easier to simplify (by factoring) BEFORE you multiply

20 What about variables? 1

21 What about higher inde numbers? 1 How many more s are needed in the denominator radicand? Remember: the cubed root of -cubed equals. We need two more s under the denominator radical. = Using the multiply powers property we don t have to write out all the individual s. 1

22 Rationalize the denominator y y

23 What about higher inde numbers? How many more s and s are needed in the denominator radicand? We need one more and two more s under the denominator radical. 1

24 What about higher inde numbers? How many more s and s are needed in the denominator radicand? We need one more s and one more under the denominator radical. 1