RADICALSTaylor Bjarnason

Introduction

I chose to do my presentation on radicals because they were my favorite chapter this year. People that could use radicals in every day life include carpenters, or roofers. Radicals are important even when launching a rocket.

Vocabulary

Mixed radical: A radical with a coefficient other than one. For example: 3 √5

Entire radical: A radical with a coefficient of 1. For example: √6

History of Radicals

The word radical come from the Latin word “radix” meaning root. The use of root comes from the mathematician Viete, he wrote about powers, calling them roots, cubes , and squares.

Identifying the index and the radicand The coefficient is referred to as the

index and the number being squared is called the radicand

index

6 5√7 radicand

Expressing a radical in simplest form

Must prime factorize!

3√40 40

= 3√2 2 2 5 2 20

Group the common number 2 10

= 2 3 √5 2 5

Expressing a mixed radical as an entire radical

4 √5

= √42 √ 5 *4 is raised to the power of

= √16 5 2 because the invisible

= √80 index is 2

Expressing an entire radical as a mixed radical

2√12 12

= 2√3 X 2 X 2 6 2

= 2 2√3 3 2

Adding and subtracting radicals

You can only add/subtract like radicals. Like radicals will have the same index

and radicand. Like radicals include: 3√5, 4 3√5, 2 3√5 Some easy examples:

2 √6 + 3√6

= 5 √6 4 4√7 - 3 4√7

= 1 4√7

Adding and subtracting radicals

Some harder examples: 2 √27 -4 √3 - √12 2 √27 27

= 6 √3 – 4 √3 – 2 √3 2 √3 3 3 3 9

= 0 √3 2 3 √3 3 3

6 √3

√12 12

√2 2 3 3 4

2 √3 2 2

Adding and subtracting radicals

2√24 –3 √96 +√432 2√24 24

= 4√6- 12√6 +12√3 2√2 2 2 3 2 12

= -8 √6 + 12 √3 2 2√6

4 √6

3√96 96

√ 2 2 2 2 2 3 6 16

√432 √432 3 4 √6 3 2 2 8

√2 2 2 2 3 3 16 27 12 √6 4 2

12√3 6 2 3 9 2 2

3 2 3 3

Multiplying and dividing radicals

Rule for multiplying radicals:

n√a n√b = n√ab You can multiply 2 radicals only if they

have the same index. Also you can only divide two radicals if

they have the same index. Rule for dividing radicals:

n√a a

n√b n√b

Multiplying radicals

√5 √6

= √5 6

=√30

3 √15 2√10

=6 √15 10

=6 √150

=6 √5 5 3 2

=30 √6

Dividing Radicals

√12

√3

=√4

= 2

4 √15

-1 √5

= -4 √3

Rationalizing the denominator

Sometimes when dividing radicals, you may get 2 radicals that do not work together. Therefore you need to rationalize the denominator. Example:

3 √7

4 √5 Since you cannot divide these you must multiply

both radicals by the denomintor.

3 √7 √5

4 √5 √5

Rationalizing the denominator

3 √7 √5

4 √5 √5

= 3 √35

4 √25

= 3 √35

4 5

= 3 √35

20