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- Elementary algebra
- Roots, radicals, and square root
- Multiplication of square root
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.Objectives of this module: be able to use the product property of square roots to multiply square roots.
Overview
- The Product Property of Square Roots
- Multiplication Rule for Square Root Expressions
The product property of square roots
In our work with simplifying square root expressions, we noted that
Since this is an equation, we may write it as
To multiply two square root expressions, we use the product property of square roots.
The product property
The product of the square roots is the square root of the product.
In practice, it is usually easier to simplify the square root expressions before actually performing the multiplication. To see this, consider the following product:
We can multiply these square roots in
either of two ways:
Notice that in the second method, the expanded term (the third expression,
) may be difficult to factor into a perfect square and some other number.
Multiplication rule for square root expressions
The preceding example suggests that the following rule for multiplying two square root expressions.
Rule for multiplying square root expressions
- Simplify each square root expression, if necessary.
- Perform the multiplecation.
- Simplify, if necessary.
Sample set a
Find each of the following products.
Practice set a
Find each of the following products.
Exercises
Exercises for review
Questions & Answers
A golfer on a fairway is 70 m away from the green, which sits below the level of the fairway by 20 m. If the golfer hits the ball at an angle of 40° with an initial speed of 20 m/s, how close to the green does she come?
A mouse of mass 200 g falls 100 m down a vertical mine shaft and lands at the bottom with a speed of 8.0 m/s. During its fall, how much work is done on the mouse by air resistance
Can you compute that for me. Ty
Jude
what is the dimension formula of energy?
Chemistry is a branch of science that deals with the study of matter,it composition,it structure and the changes it undergoes
Adjei
please, I'm a physics student and I need help in physics
Adjanou
chemistry could also be understood like the sexual attraction/repulsion of the male and female elements. the reaction varies depending on the energy differences of each given gender. + masculine -female.
Pedro
A ball is thrown straight up.it passes a 2.0m high window 7.50 m off the ground on it path up and takes 1.30 s to go past the window.what was the ball initial velocity
2. A sled plus passenger with total mass 50 kg is pulled 20 m across the snow (0.20) at constant velocity by a force directed 25° above the horizontal. Calculate (a) the work of the applied force, (b) the work of friction, and (c) the total work.
you have been hired as an espert witness in a court case involving an automobile accident. the accident involved car A of mass 1500kg which crashed into stationary car B of mass 1100kg. the driver of car A applied his brakes 15 m before he skidded and crashed into car B. after the collision, car A s
can someone explain to me, an ignorant high school student, why the trend of the graph doesn't follow the fact that the higher frequency a sound wave is, the more power it is, hence, making me think the phons output would follow this general trend?
Nevermind i just realied that the graph is the phons output for a person with normal hearing and not just the phons output of the sound waves power, I should read the entire thing next time
Joseph
Follow up question, does anyone know where I can find a graph that accuretly depicts the actual relative "power" output of sound over its frequency instead of just humans hearing
Joseph
"Generation of electrical energy from sound energy | IEEE Conference Publication | IEEE Xplore" ***ieeexplore.ieee.org/document/7150687?reload=true
Ryan
what are the types of wave
Maurice
fine, how about you?
Mohammed
A string is 3.00 m long with a mass of 5.00 g. The string is held taut with a tension of 500.00 N applied to the string. A pulse is sent down the string. How long does it take the pulse to travel the 3.00 m of the string?
Who can show me the full solution in this problem?
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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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