Simplifying Radicals 3/21

Simplifying Radicals 3/21Simplifying

Square Roots

22 = 432 = 942 = 1652 = 2562 = 3672 = 4982 = 6492 = 81102 = 100112 = 121122 = 144

These numbers in red are what we will be using to solve the questions

Mathematics.XEI.504.C: (24-27) manipulate radical expressions


Square Roots

Simplify

Starting at the bottom of your list of perfect squares, which perfect square can divide evenly into 125?

125



Square Roots

Simplify


125 / 25 = 5 * =

125

25 5 125



Square Roots

Simplify


25 * 5 = 125 * =

5 * =

125

25 5 125

5 125Mathematics.XEI.504.C: (24-27) manipulate radical expressions


Square Roots

Simplify


25 * 5 = 125 * =

5 * =Final Answer: 5

125

25 5 125

5 1255Mathematics.XEI.504.C:

(24-27) manipulate radical expressions

Simplify

1 2 3 4

25% 25%25%25%

147

1. 32. 73. 74. 3

7

73

3

600 of 30

Simplify

1 2 3 4

25% 25%25%25%

80

5

410

20

1. 42. 53. 104. 2

600 of 30

Student Practice

• Please take out a sheet of paper, label it Classwork: Simplifying Radicals & Basic Trig

• Complete the questions from the whiteboard• You have 10 minutes


Simplifying Radicals 3/21Adding /

Subtracting Radicals


You can only add or subtract if the radicand (number under the square root sign) is the same.




1. Simplify the two expressions

2. Add or subtract the coefficients, leaving the radicand the same






Example: + =________48 12






Example: + =________48 12

3448 3212






Example: + =________

Final

48 12

3448 3212

363234




You can only add or subtract if the radicand (number under the square root sign) is the same.

Example: ___________9829






Example:

These are different, can’t combine

___________9829

3329 2798






Example:

Final Answer

___________9829

3329 2798

2733

Student Practice

• Continue on your classwork page• Complete the questions from the whiteboard• You have 10 minutes


Simplifying Radicals 3/21Multiplying

Radicals


You can multiply radicals even if the radicand is different


Radicals


Multiplying radicals is a four step process:

1. Simplify both expressions.2. Multiply both coefficients.3. Multiply both radicands.4. Check to see if the resulting radicand can be reduced further.


Radicals



Example: 298


Radicals



Example: 298

228 3329


Radicals



Example:

2*3 = 6

2920

5220 3329


Radicals



Example:

2*3 = 6Answer: 6

2920

5220 3329

1535 15


Radicals



Example:

2*3 = 6Final answer: 6

2920

5220 3329

1535 15

Student Practice




Square Roots


If there are variables underneath the square root, divide the exponent by two.


Square Roots



Example: 4x


Square Roots



Example:

Divide the exponent by two, and drop the square root sign

4x


Square Roots



Example:

x2

Divide the exponent by two, and drop the square root sign

4x


Square Roots


If the exponent under the square root is odd:

7x


Square Roots



= *

Separate it into two pieces

7x 6x x


Square Roots



= *

x3 *

Simplify the even exponent

7x 6x x

x


Square Roots



= *

x3 *

Final answer: x3

7x 6x x

x

x

Simplify:

1 2 3 4

25% 25%25%25%

436x

1. . x2

2. .3. 6x2

4. 6

36436x

4x

0 of 30

60

Simplify:

1 2 3 4

25% 25%25%25%

69 yx

0 of 30

60

1. x4y3

2. x3y2

3. x3y3

4. x4y3 x

x

Student Practice



Simplifying Radicals 3/21

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