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- Elementary algebra
- Roots, radicals, and square root
- Simplifying square root expressions
To simplify a square root expression that does not involve a fraction, we can use the following two rules:
Simplifying square roots without fractions
- If a factor of the radicand contains a variable with an
even exponent, the square root is obtained by dividing the exponent by 2.
- If a factor of the radicand contains a variable with an
odd exponent, the square root is obtained by first factoring the variable factor into two factors so that one has an even exponent and the other has an exponent of 1, then using the product property of square roots.
Sample set a
Simplify each square root.
Both exponents are even:
and
The exponent on the square root of
is 3. The exponent on the square root if
is 5.
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Practice set a
Simplify each square root.
Square roots involving fractions
A square root expression is in simplified form if there are
- no perfect squares in the radicand,
- no fractions in the radicand, or
- 3. no square root expressions in the denominator.
The square root expressions
and
are in simplified form.
The square root expressions
and
are
not in simplified form.
Simplifying square roots with fractions
To simplify the square root expression
- Write the expression as
using the rule
- Multiply the fraction by 1 in the form of
- Simplify the remaining fraction,
Rationalizing the denominator
The process involved in step 2 is called
rationalizing the denominator. This process removes square root expressions from the denominator using the fact that
Sample set b
Simplify each square root.
Practice set b
Simplify each square root.
Exercises
For the following problems, simplify each of the radical expressions.
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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