Algebra
Simplifying Different Types of Radical Expressions
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SIMPLIFYING RADICALS Simplest form Similar radicals 2nd level ? Simplifying powers Factors?of the radicand Fractional radicand WE SAY THAT A SQUARE ROOT RADICAL?is?simplified, or in its?simplest form, when the?radicand?has no?square?factors. A radical is also in simplest form when the radicand isnot a fraction. Example 1.???33, for example, has no square factors. ?Its factors are 3??11, neither of which is a square number. ?Therefore,??is in its simplest form. Example 2.???18 has the square factor 9. ?18 = 9??2. ?Therefore,??is not in its simplest form.? To put a radical in its simplest form, we make use of this theorem: The square root of a product? is equal to the product of the square roots? of each factor. (We will prove that when we come to?rational exponents, Lesson 29.
algebra
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Junior Math League Competition
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The following are the 2 problems from the NVCM math league contest. The answers will be provided at the bottom.
Note: This requires knowledge and use of both geometry and algebra. Also " means the same as the previous equation.
1. The difference between two consecutive perfect squares is 739. Write the larger of these perfect squares.
Solution:
Let x^2 be the larger and (x-1)^2 be the smaller of the two squares. Then
739= x^2-(x-1)^2
"=x^2-(x^2-2x+1)
"=2x-1
740=2x
370=x
You must find the larger which is represented by x^2 so----
x^2
370^2
136,900---- Answer
2. The product of two positive, consecutive odd integers is 4623. Find the smaller integer.
Solution:
SLOPE EQUATION
Steps for Factoring Polynomials
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1. Pull out greatest common factor or GCF [This is a very important step that is often skipped] Ex: or
2. Look at number of terms
a. 2 Terms: If there are two terms (binomial), then check to see if it is
i. A difference of squares:
Ex:
ii. A difference of cubes
Ex:
iii. A sum of cubes
Ex:
If there are two terms and the expression is none of the above, it is prime!
b. 3 Terms: If there are three terms (trinomial), then factor into two binomials thinking of the FOIL method in reverse.
Find factors of c that add up to b.
Start by identifying the factors of c. The sign before c determines whether signs are the same or different in the 2 binomials that are produced, .
Quadratic Formula
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x is equal to negative (b). Plus or minus the square root of b^2 minus 4(a)(c)all over 2(a)
How to Solve problems like this (x-2)^2
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Pythagoream theroum
alegbra
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