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MATH 2A CHAPTER ELEVEN POWERPOINT PRESENTATION IRRATIONAL NUMBERS AND RADICAL EXPRESSIONS

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LEARNING TARGETS AFTER YOU COMPLETE THIS CHAPTER, YOU WILL BE ABLE TO: DISTINGUISH RATIONAL AND IRRATIONAL NUMBERS. FIND ROOTS OF RADICALS. SIMPLIFY RADICAL EXPRESSIONS. ADD, SUBTRACT, MULTIPLY, AND DIVIDE RATIONAL EXPRESSIONS. RATIONALIZE A DENOMINATOR. SOLVE EQUATIONS AND USE A GRAPH TO FIND A SQUARE ROOT.

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CHAPTER VOCABULARY IRRATIONAL NUMBER: A NON-REPEATING AND NON-TERMINATING NUMBER. RATIONAL NUMBER: A NUMBER THAT CAN BE EXPRESSED AS A RATIO OF TWO NUMBERS: INCLUDES: 0 TO INFINITY ON WHOLE NUMBERS BOTH NEGATIVE AND POSITIVE, AND REGULAR FRACTIONS. DECIMAL EXPANSION: WRITING A NUMBER SUCH AS A FRACTION AS A DECIMAL.

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MORE CHAPTER VOCABULARY TERMINATING DECIMAL EXPANSION: A DECIMAL SEQUENCE THAT ENDS IN ZERO. REPEATING DECIMAL EXPANSION: A DECIMAL SEQUENCE WHERE THE NUMBERS REPEAT IN EXACTLY THE SAME ORDER. NON-TERMINATING: DOES NOT END NON-REPEATING: IT REPEATS BUT NOT IN A SET ORDER.

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EXAMPLES: IRRATIONAL NUMBER: pi, 22 divided by 7, the square root of 2 or 3. RATIONAL: 2, -3, ½, ¼, the square root of 144. Decimal expansion: 2/5 =.40 – rational Decimal expansion: 22/7 = … - irrational. Terminating: ¼ =.250 Non-terminating: 7/11 =

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More Examples: Repeating: 1/9 = Non-repeating: 2/ We mark repeating decimals with a line above the part that repeats:

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Rational Number Equivalents Rational Number Equivalents can be calculated using an equation. Let x = the expansion written as a repeating decimal. Multiply both sides that will allow the repeating digit to go on the left of the decimal (usually 10, 100, 1000). Subtract the repeating decimal and solve the one step equation for the rational number that is equal to a repeating decimal.

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Rational Number Equivalent Example: Take: …. Set up: 10 (x) = (10) etc 10x = (use four places) -1x = x = x = 1/3 so = 1/3

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Irrational Numbers as Decimals Radical: a number that is written with the radical sign. Radical sign: Sing for approximately equal to:

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Square roots and more You can find a square root of a number but also cube roots, 4 th roots, 5 th roots, etc. Square root of 36 is 6, the square root of 49 is 7. Some square roots are irrational numbers such as the square root of 2 which is … The square root of 11 is …which is an irrational number.

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What a Cube Root Looks Like Cube root:

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Products and Quotients of Radicals You can multiply and find the quotients of radials. Let’s say you want to multiply the square root of 4 and the square root of 25. So you are really multiplying 2 times 5 = 10. If you are dividing for example: divide the square root of 64 by the square root of 144, you are really dividing 8 by 12 or 4/5.

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Examples

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Examples of Radicals in Equations

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Radicals and Fractions Rationalize the Denominator: changing a fraction with an irrational number to an equivalent fraction with a rational number. Conjugate: A factor that when multiplied rationalizes (or simplifies) an expression.

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Radicals And Exponents Radicand: a number under the radical sign. Parts of a radical:

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Square Root Graph A way to find a square root using a graph. You will set up your graph with the squares of every number from 1 to 10 on the x-axis. Then on the y-axis choose a system for numbers counting by 5’s. (Go up to at least 100) When the graph and the number of the roots you are look for align, that is the square root of that number.

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