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## RADICAL EXPRESSIONS

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**RADICAL EXPRESSIONS**ARE THE SAME AS SQUARE ROOTS**Radical Expressions**• Square Roots & Perfect Squares • Simplifying Radicals • Multiplying Radicals • Dividing Radicals • Adding Radicals**The square root of a number is a # when multiplied by itself**equals the number 64 8 8**A Square Root is a term when squared is the Perfect Square**X2 X X**Answer**64x2 8x 8x**Answer**4x2 2x 2x**What is the square root?**(x+3)2**Answer**(x+3) (x+3)2 (x+3)**Radical Sign**• This is the symbol for square root • If the number 3 is on top of the v, it is called the 3rd root.**Radical Sign**• This is the 4th root. • This is the 6th root • If n is on top of the v, it is called the nth root.**Cube Root**If the sides of a cube are 3 inches Then the volume of the cube is 3 times 3 times 3 or 33 which is 27 cubic inches.**NUMBER Perfect Squares**Numbers that are perfect squares are: 12=1, 22= 4, 32= 9, 42= 16, 52= 25, 62= 36, 72= 49, 82= 64, 92= 81, 102= 100, …**Recognizing Perfect Squares(NAME THE SQUARE ROOTS)**Variables that are perfect squares are: x2, a4, y22, x100… (Any even powered variable is a perfect square) x25 EVEN POWERED EXPONENTS ARE SQUARES x25 x50**NAME THE SQUARE ROOT**9x50**3x25**EVEN POWERED EXPONENTS ARE SQUARES 3x25 9x50**Recognizing Perfect Squares(NAME THE SQUARE ROOTS)**x2 4 25x2 4x6**Recognizing Perfect Squares(NAME THE SQUARE ROOTS)**x 2 x x2 2 4 5x 2x3 5x 25x2 2x3 4x6**Simplifying Square Roots**We can simplify if 8 contains a Perfect Square**Simplifying Square Roots**Look to factor perfect squares (4, 9, 16, 25, 36…) Put perfect squares in first radical and the other factor in 2nd. Take square root of first radical**Simplifying Square Roots**1. Factor any perfect squares (4, 9, 16, 25, x2, y6…) (Put perfect squares in first radical and other factor in 2nd)**Simplifying Square Roots**1. Factor any perfect squares (4, 9, 16, 25, x2, y6…) (& Put perfect squares in first radical and other factor in 2nd) 2. Take square root of first radical**Simplifying Square Roots**1. Factor any perfect squares (4, 9, 16, 25, x2, y6…) (& Put perfect squares in first radical and other factor in 2nd) 2. Take square root of first radical**Simplifying Square Roots**1. Factor any perfect squares (4, 9, 16, 25, x2, y6…) (& Put perfect squares in first radical and other factor in 2nd) 2. Take square root of first radical**Simplifying Square Roots**1. Factor any perfect squares (4, 9, 16, 25, 36…) (& Put perfect squares in first radical and other factor in 2nd)**Simplifying Square Roots**1. Factor any perfect squares (4, 9, 16, 25, 36…) (& Put perfect squares in first radical and other factor in 2nd) 2. Take square root of first radical**Simplifying Square Roots**1. Factor any perfect squares (4, 9, 16, 25, 36…) (& Put perfect squares in first radical and other factor in 2nd)**Simplifying Radicals**1. Factor any perfect squares (4, 9, 16, 25, 36…) (& Put perfect squares in first radical and other factor in 2nd)**Simplifying Radicals**1. Factor any perfect squares (4, 9, 16, 25, x2, y6…) (& Put perfect squares in first radical and other factor in 2nd) 2. Take square root of first radical**Simplifying Fraction Radicals**1. Factor any perfect squares (4, 9, 16, 25, x2, y6…) from NUMERATOR & DENOM. (& Put perfect squares in first radical and other factor in 2nd)**Simplifying Fraction Radicals**1. Factor any perfect squares (4, 9, 16, 25, x2, y6…) from NUMERATOR & DENOM. (& Put perfect squares in first radical and other factor in 2nd) 2. Take square root of first radical**Simplifying Fraction Radicals**1. Factor any perfect squares (4, 9, 16, 25, x2, y6…) from NUMERATOR & DENOM. (& Put perfect squares in first radical and other factor in 2nd) 2. Take square root of first radical 3. REDUCE**Finding Perfect Squares**The most common perfect squares are 4 & 9. USE DIVISIBILITY RULES: A number is divisible by 4 if the last 2 digits are divisible by 4. ( 23,732 is divisible by 4 since 32 is.) A number is divisible by 9 if the sum of it’s digits are. (4653 is divisible by 9 since the sum of it’s digits are.)**Finding Perfect Squares**MORE EASY TO FIND PERFECT SQUARES: A number with an even number of Zeros. ( 31,300 is divisible by 10, 70,000 is divisible by 100) A number ending in 25, 50 or 75 is divisible by 25. (425 & 350 & 775 are all divisible by 25)**Perfect Squares Guide Divisibility Rules for Perfect Squares**4: If Last 2 Digits are Divisible by 4 9: If Sum of Digits are Divisible by 9 16: Use 4 Rule 25: If # ends in 25, 50, 75 or 00 36: Use 4 or 9 Rule 49: Look for multiple of 50 and subtract multiple 64: Use 4 Rule 81: Use 9 Rule 100: If # ends in 00 121: No Rule, Divide # by 121 144: Use 4 or 9 Rule**Multiply Radicals**Multiply to one radical**Multiply Radicals**Multiply to one radical**Multiply Radicals**Multiply to one radical Simplify • Factor any perfect squares (4, 9, 16, x2, y6…)**Multiply Radicals**Multiply to one radical Simplify • Factor any perfect squares (4, 9, 16, x2, y6…)