simplifying radicals 3/21
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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
Simplifying Radicals 3/21Simplifying
Square Roots
Simplify
Starting at the bottom of your list of perfect squares, which perfect square can divide evenly into 125?
125
Mathematics.XEI.504.C: (24-27) manipulate radical expressions
Simplifying Radicals 3/21Simplifying
Square Roots
Simplify
Starting at the bottom of your list of perfect squares, which perfect square can divide evenly into 125?
125 / 25 = 5 * =
125
25 5 125
Mathematics.XEI.504.C: (24-27) manipulate radical expressions
Simplifying Radicals 3/21Simplifying
Square Roots
Simplify
Starting at the bottom of your list of perfect squares, which perfect square can divide evenly into 125?
125 / 25 = 5 * =
125
25 5 125
Mathematics.XEI.504.C: (24-27) manipulate radical expressions
Simplifying Radicals 3/21Simplifying
Square Roots
Simplify
Starting at the bottom of your list of perfect squares, which perfect square can divide evenly into 125?
25 * 5 = 125 * =
5 * =
125
25 5 125
5 125Mathematics.XEI.504.C: (24-27) manipulate radical expressions
Simplifying Radicals 3/21Simplifying
Square Roots
Simplify
Starting at the bottom of your list of perfect squares, which perfect square can divide evenly into 125?
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
Mathematics.XEI.504.C: (24-27) manipulate radical expressions
Simplifying Radicals 3/21Adding /
Subtracting Radicals
Mathematics.XEI.504.C: (24-27) manipulate radical expressions
You can only add or subtract if the radicand (number under the square root sign) is the same.
Simplifying Radicals 3/21Adding /
Subtracting Radicals
Mathematics.XEI.504.C: (24-27) manipulate radical expressions
1. Simplify the two expressions
2. Add or subtract the coefficients, leaving the radicand the same
Simplifying Radicals 3/21Adding /
Subtracting Radicals
Mathematics.XEI.504.C: (24-27) manipulate radical expressions
1. Simplify the two expressions
2. Add or subtract the coefficients, leaving the radicand the same
Example: + =________48 12
Simplifying Radicals 3/21Adding /
Subtracting Radicals
Mathematics.XEI.504.C: (24-27) manipulate radical expressions
1. Simplify the two expressions
2. Add or subtract the coefficients, leaving the radicand the same
Example: + =________48 12
3448 3212
Simplifying Radicals 3/21Adding /
Subtracting Radicals
Mathematics.XEI.504.C: (24-27) manipulate radical expressions
1. Simplify the two expressions
2. Add or subtract the coefficients, leaving the radicand the same
Example: + =________
Final
48 12
3448 3212
363234
Simplifying Radicals 3/21Adding /
Subtracting Radicals
Mathematics.XEI.504.C: (24-27) manipulate radical expressions
You can only add or subtract if the radicand (number under the square root sign) is the same.
Example: ___________9829
Simplifying Radicals 3/21Adding /
Subtracting Radicals
Mathematics.XEI.504.C: (24-27) manipulate radical expressions
1. Simplify the two expressions
2. Add or subtract the coefficients, leaving the radicand the same
Example:
These are different, can’t combine
___________9829
3329 2798
Simplifying Radicals 3/21Adding /
Subtracting Radicals
Mathematics.XEI.504.C: (24-27) manipulate radical expressions
1. Simplify the two expressions
2. Add or subtract the coefficients, leaving the radicand the same
Example:
Final Answer
___________9829
3329 2798
2733
Student Practice
• Continue on your classwork page• Complete the questions from the whiteboard• You have 10 minutes
Mathematics.XEI.504.C: (24-27) manipulate radical expressions
Simplifying Radicals 3/21Multiplying
Radicals
Mathematics.XEI.504.C: (24-27) manipulate radical expressions
You can multiply radicals even if the radicand is different
Simplifying Radicals 3/21Multiplying
Radicals
Mathematics.XEI.504.C: (24-27) manipulate radical expressions
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.
Simplifying Radicals 3/21Multiplying
Radicals
Mathematics.XEI.504.C: (24-27) manipulate radical expressions
1. Simplify both expressions.2. Multiply both coefficients.3. Multiply both radicands.4. Check to see if the resulting radicand can be reduced further.
Example: 298
Simplifying Radicals 3/21Multiplying
Radicals
Mathematics.XEI.504.C: (24-27) manipulate radical expressions
1. Simplify both expressions.2. Multiply both coefficients.3. Multiply both radicands.4. Check to see if the resulting radicand can be reduced further.
Example: 298
228 3329
Simplifying Radicals 3/21Multiplying
Radicals
Mathematics.XEI.504.C: (24-27) manipulate radical expressions
1. Simplify both expressions.2. Multiply both coefficients.3. Multiply both radicands.4. Check to see if the resulting radicand can be reduced further.
Example:
2*3 = 6
2920
5220 3329
Simplifying Radicals 3/21Multiplying
Radicals
Mathematics.XEI.504.C: (24-27) manipulate radical expressions
1. Simplify both expressions.2. Multiply both coefficients.3. Multiply both radicands.4. Check to see if the resulting radicand can be reduced further.
Example:
2*3 = 6Answer: 6
2920
5220 3329
1535 15
Simplifying Radicals 3/21Multiplying
Radicals
Mathematics.XEI.504.C: (24-27) manipulate radical expressions
1. Simplify both expressions.2. Multiply both coefficients.3. Multiply both radicands.4. Check to see if the resulting radicand can be reduced further.
Example:
2*3 = 6Final answer: 6
2920
5220 3329
1535 15
Student Practice
• Continue on your classwork page• Complete the questions from the whiteboard• You have 10 minutes
Mathematics.XEI.504.C: (24-27) manipulate radical expressions
Simplifying Radicals 3/21Simplifying
Square Roots
Mathematics.XEI.504.C: (24-27) manipulate radical expressions
If there are variables underneath the square root, divide the exponent by two.
Simplifying Radicals 3/21Simplifying
Square Roots
Mathematics.XEI.504.C: (24-27) manipulate radical expressions
If there are variables underneath the square root, divide the exponent by two.
Example: 4x
Simplifying Radicals 3/21Simplifying
Square Roots
Mathematics.XEI.504.C: (24-27) manipulate radical expressions
If there are variables underneath the square root, divide the exponent by two.
Example:
Divide the exponent by two, and drop the square root sign
4x
Simplifying Radicals 3/21Simplifying
Square Roots
Mathematics.XEI.504.C: (24-27) manipulate radical expressions
If there are variables underneath the square root, divide the exponent by two.
Example:
x2
Divide the exponent by two, and drop the square root sign
4x
Simplifying Radicals 3/21Simplifying
Square Roots
Mathematics.XEI.504.C: (24-27) manipulate radical expressions
If the exponent under the square root is odd:
7x
Simplifying Radicals 3/21Simplifying
Square Roots
Mathematics.XEI.504.C: (24-27) manipulate radical expressions
If the exponent under the square root is odd:
= *
Separate it into two pieces
7x 6x x
Simplifying Radicals 3/21Simplifying
Square Roots
Mathematics.XEI.504.C: (24-27) manipulate radical expressions
If the exponent under the square root is odd:
= *
x3 *
Simplify the even exponent
7x 6x x
x
Simplifying Radicals 3/21Simplifying
Square Roots
Mathematics.XEI.504.C: (24-27) manipulate radical expressions
If the exponent under the square root is odd:
= *
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
• Continue on your classwork page• Complete the questions from the whiteboard• You have 10 minutes
Mathematics.XEI.504.C: (24-27) manipulate radical expressions
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