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- Elementary algebra
- Roots, radicals, and square root
- Summary of key concepts
This module is from Elementary Algebra by Denny Burzynski and Wade Ellis, Jr.
The distinction between the principal square root of the number x and the secondary square root of the number x is made by explanation and by example. The simplification of the radical expressions that both involve and do not involve fractions is shown in many detailed examples; this is followed by an explanation of how and why radicals are eliminated from the denominator of a radical expression. Real-life applications of radical equations have been included, such as problems involving daily output, daily sales, electronic resonance frequency, and kinetic energy.This module presents a summary of the key concepts of the chapter "Roots, Radicals, and Square Root Equations".
Summary of key concepts
Square root (
[link] )
The square root of a positive number
is a number such that when it is squared, the number
results.
Every positive number has two square roots, one positive and one negative. They are opposites of each other.
Principal square root
(
[link] )
If
is a positive real number, then
represents the positive square root of
. The positive square root of a number is called the
principal square root of the number.
Secondary square root
(
[link] )
represents the negative square root of
. The negative square root of a number is called the
secondary square root of the number.
Radical sign, radicand; and radical (
[link] )
In the expression
√ is called the
radical sign .
is called the
radicand .
is called a
radical .
The horizontal bar that appears attached to the radical sign, √, is a grouping symbol that specifies the radicand.
Meaningful expressions (
[link] )
A radical expression will only be meaningful if the radicand (the expression under the radical sign) is
not negative:
is not meaningful and
is not a real number
Simplifying square root expressions (
[link] )
If
is a nonnegative number, then
Perfect squares (
[link] )
Real numbers that are squares of rational numbers are called
perfect squares .
Irrational numbers (
[link] )
Any indicated square root whose radicand is not a perfect square is an irrational number.
and
are irrational numbers
The product property (
[link] )
The quotient property (
[link] )
Be careful (
[link] )
A square root that does not involve fractions is in simplified form if there are no perfect squares in the radicand.
A square root involving a fraction is in simplified form if there are no
- perfect squares in the radicand,
- fractions in the radicand, or
- square root expressions in the denominator
Rationalizing the denominator (
[link] )
The process of eliminating radicals from the denominator is called
rationalizing the denominator .
Multiplying square root expressions (
[link] )
The product of the square roots is the square root of the product.
- Simplify each square root, if necessary.
- Perform the multiplication.
- Simplify, if necessary.
Dividing square root expressions (
[link] )
The quotient of the square roots is the square root of the quotient.
Addition and subtraction of square root expressions (
[link] )
Square root equation (
[link] )
A
square root equation is an equation that contains a variable under a square root radical sign.
Solving square root equations (
[link] )
- Isolate a radical.
- Square both sides of the equation.
- Simplify by combining like terms.
- Repeat step 1 if radical are still present.
- Obtain potential solution by solving the resulting non-square root equation.
- Check potential solutions by substitution.
Questions & Answers
number of sport play by 50 student construct discrete data
width of the frangebany leaves on how to write a introduction
Solve the mean of variance
Step 1: Find the mean. To find the mean, add up all the scores, then divide them by the number of scores. ...
Step 2: Find each score's deviation from the mean. ...
Step 3: Square each deviation from the mean. ...
Step 4: Find the sum of squares. ...
Step 5: Divide the sum of squares by n – 1 or N.
kenneth
Is mistake done to something
Vutshila
What is the life teble
anas
statistics is the analyzing of data
how do you calculate mean
diveving the sum if all values
Shaynaynay
let A1,A2 and A3 events be independent,show that (A1)^c, (A2)^c and (A3)^c are independent?
data collected all over the world
Shaynaynay
construct a less than and more than table
The sample of 16 students is taken. The average age in the sample was 22 years with astandard deviation of 6 years. Construct a 95% confidence interval for the age of the population.
Bhartdarshan' is an internet-based travel agency wherein customer can see videos of the cities they plant to visit. The number of hits daily is a normally distributed random variable with a mean of 10,000 and a standard deviation of 2,400
a. what is the probability of getting more than 12,000 hits?
b. what is the probability of getting fewer than 9,000 hits?
Bhartdarshan'is an internet-based travel agency wherein customer can see videos of the cities they plan to visit. The number of hits daily is a normally distributed random variable with a mean of 10,000 and a standard deviation of 2,400.
a. What is the probability of getting more than 12,000 hits
Akshay
Sorry i want to learn more about this question
Bright
a= 0.20233
b=0.3384
Sufiyan
How do I interpret level of significance?
It depends on your business problem or in Machine Learning you could use ROC- AUC cruve to decide the threshold value
Shivam
how skewness and kurtosis are used in statistics
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Source:
OpenStax, Elementary algebra. OpenStax CNX. May 08, 2009 Download for free at http://cnx.org/content/col10614/1.3
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