7 4 Study Guide And Intervention Radical Expressions

7 4 Study Guide And Intervention Radical Expressions Chapter 7 23 Glencoe Algebra 1 7 4 Study Guide and Intervention Scientific Notation Scientific Notation Very large and very small numbers are often best represented using a method known as scientific notation Numbers written in scientific notation take the form a 10 where 1 a 10 and n is an integer Any number

Radical expressionsif both the indices and the radicands are alike To multiply radicals use the Product and Quotient Properties For products of the form 10 2 10 5 Combine like radicals Study Guide and Intervention continued Radical Expressions NAME DATE PERIOD 5 65 6 ExampleExample11 Simplify 2 3 4 2 3 2 Study Guide and Intervention Radical Expressions Propert ies of Square Roots The Product Property of Square Roots and prime factorization can be used to simplify expressions involving irrational square roots When you simplify radical expressions with variables use absolute value to ensure nonnegative results

7 4 Study Guide and Intervention nth Roots continued Approximate Radicals with a Calculator Radicals such as 2 and 3 are examples of irrational numbers Decimal approximations for irrational numbers are often used in applications These approximations can be easily found with a calculator Example Use a calculator to approximate

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7 4 Study Guide And Intervention Radical Expressions

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7 4 Study Guide And Intervention Radical Expressions

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Chapter 7 24 Glencoe Geometry Study Guide and Intervention Parallel Lines and Proportional Parts Proportional Parts within Triangles In any triangle a line parallel to one side of a triangle separates the other two sides proportionally This is the Triangle Proportionality Theorem The converse is also true If XY RS then RX XT

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Operations with Radical Expressions Add or Subtract Radical Expressions When adding or subtracting radical expressions use the Associative and Distributive Properties to simplify the expressions If radical expressions are not in simplest form simplify them Example 1 Simplify 10 6 5 3 6 3 4 6

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1 a number decreased by 82 a number divided by 8 3 a number squared4 four times a number 5 a number divided by 66 a number multiplied by 37 7 the sum of 9 and a number8 3 less than 5 times a number 9 twice the sum of 15 and a number10 one half the square of b 11 7 more than the product of 6 and a number

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Lesson 7 4 Chapter 7 23 Glencoe Algebra 1 Study Guide and Intervention Scientifi c Notation 7 4 Scientific Notation Very large and very small numbers are often best represented using a method known as scientific notation Numbers written in scientific notation take the form a 10n where 1 a 10 and n is an integer Any number can be

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2 1 Study Guide and Intervention Power and Radical Functions PERIOD Radical Functions and Equations A radical function is a thnction that has at least one radical expression containing the indeFndent satiable For example Rx is a tadical function A radical equation is an equation in SShich the variable is in the radicands To solve a radical eq

7 3 Study Guide and Intervention Rational Exponents Rational Exponents For any real numbers a and b and any positive integer n if an b then a is an nth root of b Rational exponents can be used to represent nth roots Example 1 Write 1 6xy 2 in radical Example 2 1 Simplify 625 4 form 1 6xy 2 6xy Defi nition of b 2 1 Simplifying Radical Expressions Product Property of Square Roots The Product Property of Square Roots and prime factorization can be used to simplify expressions involving irrational square roots When you simplify radical expressions with variables use absolute value to ensure nonnegative results Product Property of Square Roots

7 4 DATE PERIOD Study Guide and Intervention continued Scientific Notation Products and Quotients in Scientific Notation You can use scientific notation to simplify multiplying and dividing very large and very small numbers Example 4 x 108 Express the result in both scientific notation and standard form uExampIeQ2 Evaluate 6 9 x 105