Algebra II 7
Algebra II
7.3 Binomial Radical Expressions
Radical expressions with the same index and the same radicand may be added or subtracted.
Add or subtract:
May need to simplify before adding or subtracting.
Assignment: page 382383, #112
7.3 continued
Multiplying Binomial Radical Expressions
Use FOIL to multiply, simplify.
Multiply:
Conjugates are expressions such as:
Just as (ab)(a+b) = a2b2
The product of conjugates is a rational number.
Simplify:
Assignment: page 382383, # 1322
7.3 continued
Dividing Binomial Radical Expressions
Recall: A real number is the result when conjugates are multiplied
2 5 = 3
To rationalize a denominator with a binomial radical multiply both denominator and numerator by the denominator's conjugate
Rational the following division problems:
Assignment: page 382383, # 2339 odd
Algebra II
7.4 Rational Exponents
Simplifying Expressions with Rational Exponents
Alternate way of writing radical expressions is to use rational(fractional) exponents. numerator of the rational exponent is the exponent denominator of the rational exponent is the root.
Rewrite:
Simplify:
rational exponents may have a numerator other than 1
Convert to radical form:
Write in exponential form:
Recall Properties for exponents:
Simplify using rational exponents:
Write in simplest form:
Assignment: page 388389, #125 odd, 4043
Algebra II
7.5 Solving Square Root and other Radical Equations
Isolate the root on one side and take both side to the power of the root
Solve:
To solve equations using rational exponents take each side to the exponents reciprocal after isolating the term to the rational exponent.
7.5 Continued
When solving equations with radical or rational exponents check for extraneous roots.
(extraneous: roots that do not make the equation true)
Extra roots that are not true are found when x is taken to a power.
Solve:
Solve :
Assignment: Pages 394395, # 127 odd
7.3 Binomial Radical Expressions
Radical expressions with the same index and the same radicand may be added or subtracted.
Add or subtract:
May need to simplify before adding or subtracting.
Assignment: page 382383, #112
7.3 continued
Multiplying Binomial Radical Expressions
Use FOIL to multiply, simplify.
Multiply:
Conjugates are expressions such as:
Just as (ab)(a+b) = a2b2
The product of conjugates is a rational number.
Simplify:
Assignment: page 382383, # 1322
7.3 continued
Dividing Binomial Radical Expressions
Recall: A real number is the result when conjugates are multiplied
2 5 = 3
To rationalize a denominator with a binomial radical multiply both denominator and numerator by the denominator's conjugate
Rational the following division problems:
Assignment: page 382383, # 2339 odd
Algebra II
7.4 Rational Exponents
Simplifying Expressions with Rational Exponents
Alternate way of writing radical expressions is to use rational(fractional) exponents. numerator of the rational exponent is the exponent denominator of the rational exponent is the root.
Rewrite:
Simplify:
rational exponents may have a numerator other than 1
Convert to radical form:
Write in exponential form:
Recall Properties for exponents:
Simplify using rational exponents:
Write in simplest form:
Assignment: page 388389, #125 odd, 4043
Algebra II
7.5 Solving Square Root and other Radical Equations
Isolate the root on one side and take both side to the power of the root
Solve:
To solve equations using rational exponents take each side to the exponents reciprocal after isolating the term to the rational exponent.
7.5 Continued
When solving equations with radical or rational exponents check for extraneous roots.
(extraneous: roots that do not make the equation true)
Extra roots that are not true are found when x is taken to a power.
Solve:
Solve :
Assignment: Pages 394395, # 127 odd