Download presentation

1
**The Radical Square Root**

The square root of any real number is a number, rational or irrational, that when multiplied by itself will result in a product that is the original number The Radical Radical sign Square Root Radicand Every positive radicand has a positive and negative sq. root. The principal Sq. Root of a number is the positive sq. root. A rational number can have a rational or irrational sq. rt. An irrational number can only have an irrational root.

2
**= 7.9 = 232 225 = +15 529 = +23 Model Problems**

Find to the nearest tenth: = 13.4 = 7.9 = 11.4 = 232 = 64.4 Find the principal Square Root: 225 = +15 529 = +23 Simplify: = |x| = x = 2x8 = x + 1

3
**Index of 2 Square Root Index of 2 radical sign radicand index**

of a number is one of the two equal factors whose product is that number Square Root Index of 2 has an index of 2 Every positive real number has two square roots The principal square root of a positive number k is its positive square root, If k < 0, is an imaginary number

4
**Index of 3 Cube Root Index = 3 radical sign radicand index**

of a number is one of the three equal factors whose product is that number has an index of 3 principal cube roots

5
nth Root The nth root of a number (where n is any counting number) is one of n equal factors whose product is that number. k is the radicand n is the index is the principal nth root of k 25 = 32 (-2)5 = -32 54 = 625

6
**Index of n nth Root Index of n radical sign radicand index**

of a number is one of n equal factors whose product is that number nth Root Index of n has an index where n is any counting number principal odd roots principal even roots

7
Radical Rules! True or False: T T T

8
**In general, for non-negative numbers a, b and n**

Radical Rule #1 In general, for non-negative numbers a, b and n Example: simplified = x4 = x3 Hint: will the index divide evenly into the exponent of radicand term?

9
**In general, for non-negative numbers a, b, and n**

Radical Rule #2 True or False: If and T T Transitive Property of Equality If a = b, and b = c, then a = c then In general, for non-negative numbers a, b, and n Example:

10
**Perfect Squares – Index 2**

12 144 11 121 100 10 9 81 8 64 7 49 6 36 5 25 4 16 3 9 4 2 1

11
**Perfect Square Factors**

Find as many combinations of 2 factors whose product is 75 Factors that are Perfect Squares Find as many combinations of 2 factors whose product is 128

12
**Find as many combinations of 2 factors whose product is 80**

Simplifying Radicals Simplify: answer must be in radical form. Find as many combinations of 2 factors whose product is 80 perfect square comes out from under the radical To simplify a radical find, if possible, 2 factors of the radicand, one of which is the largest perfect square of the radicand. The square root of the perfect square becomes a factor of the coefficient of the radical.

13
Perfect Cubes 13 = 23 = 33 = 43 = 53 = 63 = 73 = (x4)3 = x12 (-2y2)3 = -8y6

14
**Simplifying Radicals Simplify: answer must be in radical form.**

1) Factor the radicand so that the perfect power (cube) is a factor 2) Express the radical as the product of the roots of the factors 3) Simplify the radical containing the largest perfect power (cube)

15
**Simplifying Radicals Simplify:**

1) Change the radicand to an equivalent fraction whose denominator is a perfect power. 2) Express the radical as the quotient of two roots 3) Simplify the radical in the denominator

16
**Simplify: Model Problems**

KEY: Find 2 factors - one of which is the largest perfect square possible

17
Model Problems Simplify:

Similar presentations

OK

or –5 The side length of a square is the square root of its area.

or –5 The side length of a square is the square root of its area.

© 2018 SlidePlayer.com Inc.

All rights reserved.

By using this website, you agree with our use of **cookies** to functioning of the site. More info in our Privacy Policy and Google Privacy & Terms.

Ads by Google

Ppt on classical economics today Ppt on centring meditation Ppt on bluetooth hacking app Ppt on hiv aids basics Ppt on apache web server Ppt on geography of world Ppt on 7 wonders of the world free download Ppt on pin diode spice Ppt on breast cancer treatment Circulatory system anatomy and physiology ppt on cells