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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
Ayele, K., 2003. Introductory Economics, 3rd ed., Addis Ababa.
can you send the book attached ?
Ariel
the study of how humans make choices under conditions of scarcity
AI-Robot
U(x,y) = (x×y)1/2
find mu of x for y
U(x,y) = (xÃy)1/2
find mu of x for y
Desalegn
this is the study of how the society manages it's scarce resources
Belonwu
macroeconomic is the branch of economics which studies actions, scale, activities and behaviour of the aggregate economy as a whole.
husaini
difference between firm and industry
what's the difference between a firm and an industry
Abdul
firm is the unit which transform inputs to output where as industry contain combination of firms with similar production 😅😅
Abdulraufu
Suppose the demand function that a firm faces shifted from
Qd 120 3P
to
Qd 90 3P
and the supply function has shifted from
QS
20 2P
to
QS
10 2P .
a) Find the effect of this change on price and quantity.
b) Which of the changes in demand and supply is higher?
explain standard reason why economic is a science
factors influencing supply
scares
means__________________ends
resources. unlimited
Jan
economics is a science that studies human behaviour as a relationship b/w ends and scares means which have alternative uses
Jan
calculate the profit maximizing for demand and supply
Why qualify 28 supplies
Milan
out-of-pocket costs for a firm, for example, payments for wages and salaries, rent, or materials
AI-Robot
concepts of supply in microeconomics
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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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