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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
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, Elementary algebra. OpenStax CNX. May 08, 2009 Download for free at http://cnx.org/content/col10614/1.3
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