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HOW DO WE SIMPLIFY RADICALS? 1. simplify square roots, and 2. simplify radical expressions.

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Presentation on theme: "HOW DO WE SIMPLIFY RADICALS? 1. simplify square roots, and 2. simplify radical expressions."— Presentation transcript:

1 HOW DO WE SIMPLIFY RADICALS? 1. simplify square roots, and 2. simplify radical expressions.

2 In the expression, is the radical sign and 64 is the radicand. If x 2 = y then x is a square root of y. 1. Find the square root: 8 2. Find the square root: -0.2

3 11, -11 4. Find the square root: 21 5.Find the square root: 3. Find the square root:

4 6.82, -6.82 6. Use a calculator to find each square root. Round the decimal answer to the nearest hundredth.

5 1 1 = 1 2 2 = 4 3 3 = 9 4 4 = 16 5 5 = 25 6 6 = 36 49, 64, 81, 100, 121, 144,... What numbers are perfect squares?

6 1. Simplify Find a perfect square that goes into 147.

7 2. Simplify Find a perfect square that goes into 605.

8 Simplify 1.. 2.. 3.. 4..

9 Look at these examples and try to find the pattern… How do you simplify variables in the radical? What is the answer to ? As a general rule, divide the exponent by two. The remainder stays in the radical.

10 Find a perfect square that goes into 49. 4. Simplify 5. Simplify

11 Simplify 1.3x 6 2.3x 18 3.9x 6 4.9x 18

12 What are Perfect Cubes? 1 3 = 1 x 1 x 1 = 1 2 3 = 2 x 2 x 2 = 8 3 3 = 3 x 3 x 3 = 27 4 3 = 4 x 4 x 4 = 64 5 3 = 5 x 5 x 5 = 125 and so on and on and on…..

13 2 2 2 x 2 = 4

14 3 x 3 = 9 3 3

15 4 x 4 = 16 4 4

16 5 5 5 x 5 = 25

17 The square root of 4 is 2

18 The square root of 9 is 3

19 The square root of 16 is 4

20 The square root of 25 is 5

21 12 34 56 78 Cubes

22 2 2 2 2 x 2 x 2 = 8

23 3 x 3 x 3 = 27

24 NTH ROOTS a square (second) root is written as: a cube (third) root is written as: a fourth root is written as: a fifth root is written as:

25 SIMPLIFY 1. 2. 3.

26 ANSWERS 1.7 2.-2 3.3xy 2

27 ASTRONOMY A special form of Kepler’s Third Law of Planetary Motion is given by where a is the average distance of an object from the Sun in AU (astronomical units) and P is the period of the orbit in years. If an object is orbiting the Sun with a period of 12 years, what is its distance from the Sun?

28 This powerpoint was kindly donated to www.worldofteaching.com www.worldofteaching.com http://www.worldofteaching.comhttp://www.worldofteaching.com is home to over a thousand powerpoints submitted by teachers. This is a completely free site and requires no registration. Please visit and I hope it will help in your teaching.


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