All Algebra II Resources
Example Questions
Example Question #22 :Irrational Numbers
Write the following expression in the standard form for a complex number
Multiply Binomials ( you may use the FOIL method)
We know that, so we replacewith
combine like terms
Distribute the i
We know that, so we replacewith
Swich to standard form
Example Question #23 :Irrational Numbers
What is the sum ofand?
Distribute the negative
Combine like terms
Example Question #24 :Irrational Numbers
Add and combine:
To simplify the irrational numbers as a single fraction, we will need a common denominator by multiplying the denominators together.
The termis the common denominator. Convert the fractions.
The answer is:
Example Question #25 :Irrational Numbers
Which of the following is considered an irrational number?
The irrational numbers do not have a representation of a ratio between two numbers. They cannot be expressed by a fraction.
Repeating decimal numbers are not irrational because they can be rewritten as a fraction.
For instance:
The numbermay represent the short version of, but is not irrational, becauseis a fixed number and be rewritten as a ratio between two numbers.
The answer is:
Example Question #61 :Number Theory
The complex conjugate for an irrational binomial number with a radical is simply the original with the sign of the radical changed.
Example Question #62 :Number Theory
Which of the below is a rational number?
Example Question #63 :Number Theory
Example Question #64 :Number Theory
Which of the following is an irrational number?
Irrational numbers cannot be expressed as a ratio of two numbers. They can be decimal numbers that go on forever without repeating.
Do not mix fixed numbers with symbolic values such asand.
The value of the sine angleis, which is not irrational.
Square root numbers and complex numbers might not necessary be irrational after their simplified form.
The correct answer is:
Example Question #30 :Irrational Numbers
Which of the following numbers are irrational?
Irrational numbers are numbers that cannot be rewritten as a fraction of two numbers.
Be careful with numbers that may look as though they are irrational, such as, but is rational since this number is finite and can be expressed as a fraction.
Irrational numbers cannot include continuous numbers such as, and some radical numbers such as.
Some of the radicals in the answers are not fully simplified.
The termcan be simplified to a whole number two, which means that this is a rational number.
The correct answer is:
Example Question #65 :Number Theory
Which of the below is NOT an irrational number?
The correct choice involves two perfect squares which makes each number a rational number:
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