Transcript Unit #3 Radicals - GHP

Radicals
• Simplify radical expressions using the
properties of radicals
• Multiplying and dividing radical
expressions using the properties of
radicals
• Adding and subtracting radical
expressions using the properties of
radicals
Radical Notation
n
a  b means a  b
n
n is called the index number
a is called the radicand
Properties of Radicals
Simplifying Radicals
1. The radicand has no factor raised to a power
greater than or equal to the index number
2. The radicand has no fractions
3. No denominator contains a radical
4. Exponents in the radicand and the index of
the radical have no common factor
5. All indicated operations have been performed
Simplify the following
expressions
Simplifying Radicals
• If there is no index #, it is understood to
be 2
• When simplifying radicals use perfect
squares, cubes, etc.
• Use factor trees to break a number into
its prime factors
• Apply the properties of radicals and
exponents
Simplify each of the following radicals.
Assume that all variables represent
nonnegative real numbers.
5.
3
128
Simplify each of the following radicals.
Assume that all variables represent
nonnegative real numbers.
Rewrite each of the following as a
single number under the radical
sign
Multiplying Radicals
1. Radicals must have the same index
number
2. Multiply outsides and insides together
3. Add exponents when multiplying
4. Simplify your expression
5. Combine all like terms
Simplify each of the following radicals.
Assume that all variables represent
nonnegative real numbers.
Dividing Radicals
1.No radicals in the denominator
2.No fractions under the radical
sign
3.Apply the properties of radicals
and exponents
Simplify each of the following radicals.
Assume that all variables represent
nonnegative real numbers and that no
denominators are zero.
Simplify each of the following radicals.
Assume that all variables represent
nonnegative real numbers and that no
denominators are zero.
Add/Subtract
Radicals
1. Simplify each
radical expression
2. Radicals must have the same index
number and same radicand
3. Add the outside numbers together and
the radicand remains the same
Simplify each of the following
radicals3
3
1. 4 128  7 54
2. 6 24  3 54  4 81
3
3
3
3. 7 45  3 80
4. 2 72  9 27  7 48  4 32
Mult/Dividing
Radicals
Simplify each of the following
radicals
53 2
3.
43 2
Mult/Dividing
Radicals
1.Multiply using fractional exponents
and the properties of exponents.
Write your answer in radical form
and simplify.
2.Multiply by changing the radicals to
a common index and simplify.