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- Radicals and rational expressions
Simplifying rational exponents
Simplify:
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Key concepts
- The principal square root of a number
is the nonnegative number that when multiplied by itself equals
See
[link] .
- If
and
are nonnegative, the square root of the product
is equal to the product of the square roots of
and
See
[link] and
[link] .
- If
and
are nonnegative, the square root of the quotient
is equal to the quotient of the square roots of
and
See
[link] and
[link] .
- We can add and subtract radical expressions if they have the same radicand and the same index. See
[link] and
[link] .
- Radical expressions written in simplest form do not contain a radical in the denominator. To eliminate the square root radical from the denominator, multiply both the numerator and the denominator by the conjugate of the denominator. See
[link] and
[link] .
- The principal
n th root of
is the number with the same sign as
that when raised to the
n th power equals
These roots have the same properties as square roots.
See
[link] .
- Radicals can be rewritten as rational exponents and rational exponents can be rewritten as radicals. See
[link] and
[link] .
- The properties of exponents apply to rational exponents. See
[link] .
Section exercises
Verbal
What does it mean when a radical does not have an index? Is the expression equal to the radicand? Explain.
When there is no index, it is assumed to be 2 or the square root. The expression would only be equal to the radicand if the index were 1.
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Numeric
For the following exercises, simplify each expression.
Algebraic
For the following exercises, simplify each expression.
Real-world applications
A guy wire for a suspension bridge runs from the ground diagonally to the top of the closest pylon to make a triangle. We can use the Pythagorean Theorem to find the length of guy wire needed. The square of the distance between the wire on the ground and the pylon on the ground is 90,000 feet. The square of the height of the pylon is 160,000 feet. So the length of the guy wire can be found by evaluating
What is the length of the guy wire?
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Extensions
For the following exercises, simplify each expression.
Questions & Answers
find the equation of the tangent to the curve y=2x³-x²+3x+1 at the points x=1 and x=3
derivative of logarithms function
how to solve this question
sidra
ex 2.1 question no 11
khansa
anyone can help me
khansa
ex 2.1 question no. 11
khansa
Find the derivative of g(x)=−3.
any genius online ? I need help!!
need to learn polynomial
Zakariya
plz help me in question
Abish
evaluate the following computation (x³-8/x-2)
teach me how to solve the first law of calculus.
teach me also how to solve the first law of calculus
Bilson
only god knows😂
abdulkadir
f(x) = x-2
g(x) = 3x + 5
fog(x)?
f(x)/g(x)
fog(x)= f(g(x))
= x-2
= 3x+5-2
= 3x+3
f(x)/g(x)= x-2/3x+5
diron
pweding paturo nsa calculus?
jimmy
how to use fundamental theorem to solve exponential
find the bounded area of the parabola y^2=4x and y=16x
what is absolute value means?
(mathematics) For a complex number a+bi, the principal square root of the sum of the squares of its real and imaginary parts, √a2+b2 . Denoted by | |.
The absolute value |x| of a real number x is √x2 , which is equal to x if x is non-negative, and −x if x is negative.
Ismael
find integration of loge x
find the volume of a solid about the y-axis, x=0, x=1, y=0, y=7+x^3
Can calculus give the answers as same as other methods give in basic classes while solving the numericals?
y=(x^2 + 3x).(eipix)
Claudia
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Source:
OpenStax, College algebra. OpenStax CNX. Feb 06, 2015 Download for free at https://legacy.cnx.org/content/col11759/1.3
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