Algebra II 6.1-6.5
Property nth roots of nth powers
For any real number a, ^n√a^n=a or |a|
Plug back in the different values for x and the ones that work are the answers
How do you check for extraneous solutions
Like any other binomial
How do you multiply binomial radicals
Multiply the top and bottom by a radical with the same index as that of the denominator and add exponents to the terms in the radical that would get it to easily solve based off the index of the radical
How do you rationalize the denominator
Raise each side of the equation to the reciprocal of the exponent, n/m
How do you solve an equation in the form of x^m/n=k
Get rid of one radical at a time usually the one with the largest radicand first by squaring both sides of the equation
How do you solve an equation with multiple radicals
The nth root
If a^n=b with a and b real numbers and n a positive integer then a is an nth root of b
lxl
If m is even in the equation (x^m/n)^n/m, what does it equal
0
If m is negative in these what can a not equal: a^m/n=^n√a^m=(^n√a)^m
Postive and negative (2)
If the index is even and the radicand is positive there are how many real nth roots and what are they
1
If the index is odd how many real nth roots are there
^3/(12y^2z)^2 or ^3/12^2yz^2
If this was in the denominator ³√12y²z what are the two ways you could rationalize it
a^2b^3
Simplify this: ^3√a^6b^9
Principal root
The positive root of a radical with an even index and a positive radicand
^n/a^m=(^n/a)^m
What are the two radical forms of a^m/n let / in your answer be a radical sign
a^m/b^m
What does (a/b)^m equal
a^mn
What does (a^m)^n equal
a^mb^m
What does (ab)^m equal
^n/ab
What does ^n√a ×^n√b equal if ^n√a and ^n√b are real numbers and b is not equal to 0
^n/(a/b)
What does ^n√a/^n√b equal if ^n√a and ^n√b are real numbers and b is not equal to 0
a^m+n
What does a number with the same base and different exponent times a number with the same base and different exponent equal a^m × a^n
1/a^m
What does a^-m equal
a^m-n
What does a^m/a^n equal
x^1/n
What is the exponent form of ^n√x
Beginning
When determining if you should use an absolute value or not what part of the equation do you look at?
Index even, there is a variable under the radical, it starts with all even exponents and an answer with an odd exponent
When do you use absolute values around your answer
When the denominator is something plus or minus a radical
When do you use conjugates
When they have the same radicand and index
When is the only time you can add/subtract radicals
No
When to use absolute value around answer: Index odd
Maybe
When to use absolute value around answer: Index even
No
When to use absolute value around answer: Index even and there is a number under radical
Maybe
When to use absolute value around answer: Index even and there is a variable under the radical
Maybe
When to use absolute value around answer: Index even, there is a variable under the radical and it starts with all even powers
No
When to use absolute value around answer: Index even, there is a variable under the radical and it starts with at least one odd exponent
No
When to use absolute value around answer: Index even, there is a variable under the radical, it starts with all even exponents and an answer with an even exponent
Yes add absolute value
When to use absolute value around answer: Index even, there is a variable under the radical, it starts with all even exponents and an answer with an odd exponent
Index
n in both radicals
Radicand
the number under the radical sign -25
