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There are four types of radicals: There are four types of radicals: √4 Radicals with a perfect square There are four types of radicals: √4 √12 Radicals with a perfect square Radicals that have a factor that is a perfect square There are four types of radicals: √4 √12 √13 Radicals with a perfect square Radicals that have a factor that is Radicals that do not have a factor that is a perfect square a perfect square There are four types of radicals: √4 √12 √13 √-1 Radicals with a perfect square Radicals that have a factor that is Radicals that do not have a factor that is Radicals that have a negative number a perfect square a perfect square Match √4 ? √-1 ? Radicals that have a negative number Radicals with a perfect square Radicals that have a perfect square are easy: Radicals that have a perfect square are easy: √4 Radicals that have a perfect square are easy: √4 Just solve for the square root of the number Radicals that have a perfect square are easy: √4 = 2 Just solve for the square root of the number Find the answer √9 = 3 Find the answer √9 = 3 √100 = 10 Find the answer √9 = 3 √100 = 10 √25 = 5 Radicals that have a factor of a perfect square are more difficult Radicals that have a factor of a perfect square √12 are more difficult Radicals that have a factor of a perfect square √12 are more difficult First find the set of factors that has the perfect square Radicals that have a factor of a perfect square 2•6 = 12 √12 are more difficult Neither 2 nor 6 is a perfect square First find the set of factors that has the perfect square Radicals that have a factor of a perfect square 3•4 = 12 2•6 = 12 √12 are more difficult Four is a perfect square First find the set of factors that has the perfect square Radicals that have a factor of a perfect square 3•4 = 12 √12 = √4•√3 are more difficult First find the set of factors that has Then split the number into the perfect square those factors Radicals that have a factor of a perfect square √12 = √4•√3 are more difficult First find the set of factors that has Then split the number into Finally, simplify the radical the perfect square those factors with the perfect square Radicals that have a factor of a perfect square √4 = 2 √12 = √4•√3 are more difficult First find the set of factors that has Then split the number into Finally, simplify the radical the perfect square those factors with the perfect square Radicals that have a factor of a perfect square √12 = √4•√3 = 2√3 are more difficult First find the set of factors that has Then split the number into Finally, simplify the radical the perfect square those factors with the perfect square Which set of factors has the perfect square 2•10 4•5 √20 Which set of factors has the perfect square So we split the number into 4• √20 Which set of factors has the perfect square √20 = √4 • √5 = √4 is a perfect square - Simplify it. √5 Radicals that don't have a perfect square factor: Radicals that don't have a perfect square factor: √21 Radicals that don't have a perfect square factor: √21 are easy because there isn't any way to simpify Radicals that don't have a perfect square factor: √21 the only set of factors for 21 are easy because there isn't (other than 1•21) are 3 and 7 any way to simpify Radicals that don't have a perfect square factor: 3•7 √21 the only set of factors for 21 are easy because there isn't (other than 1•21) are 3 and 7 any way to simpify Radicals that don't have a perfect square factor: 3•7 √21 Since neither 3 nor 7 are perfect squares the only set of factors for 21 are easy because there isn't (other than 1•21) are 3 and 7 any way to simpify Radicals that don't have a perfect square factor: 3•7 √21 Since neither 3 nor 7 are perfect squares there isn't any way to simplify the only set of factors for 21 are easy because there isn't (other than 1•21) are 3 and 7 any way to simpify Radicals that don't have a perfect square factor: 3•7 √21 = √21 Since neither 3 nor 7 are perfect squares So it just stays √21 there isn't any way to simplify the only set of factors for 21 are easy because there isn't (other than 1•21) are 3 and 7 any way to simpify Solve √26 = √26 Solve √26 = √26 √51 = √51 Solve √26 = √26 √51 = √51 √6 = √6 Which of these number is a perfect square? 3 64 99 149 Which of these number is a perfect square? 5 47 49 125 The first 15 perfect squares are as follows:1, 4, 9, 16, 25, 36, 49, 64, 81, 100, 121, 144, 169, 196, 225. They keep going; however, these are the main ones we use. What perfect square is inside 99? The first 15 perfect squares are as follows:1, 4, 9, 16, 25, 36, 49, 64, 81, 100, 121, 144, 169, 196, 225. They keep going; however, these are the main ones we use. What perfect square is inside 8? The first 15 perfect squares are as follows:1, 4, 9, 16, 25, 36, 49, 64, 81, 100, 121, 144, 169, 196, 225. They keep going; however, these are the main ones we use. What perfect square is inside 125? The first 15 perfect squares are as follows:1, 4, 9, 16, 25, 36, 49, 64, 81, 100, 121, 144, 169, 196, 225. They keep going; however, these are the main ones we use. What perfect square is inside 24? √20 = √4 • √5 = 2√5 Solve √20 = √4 • √5 = 2√5 √100 = 10 Solve √20 = √4 • √5 = 2√5 √100 = 10 √33 = √ Solve √20 = √4 • √5 = 2√5 √100 = 10 √33 = √33 √8 = 2√2 Solve Simplify the following: √125 = √60 √27 = √68 = = √ √ √ √ Negative radicals are not real as no number multiplied by itself can be negative. There are four types of radicals: √12 √13 √4 In summary... √-1 =2 = 2√3 =√13 not real Radicals that do not have a factor that is Radicals that have a negative number Radicals that have a factor that is Radicals with a perfect square a perfect square a perfect square |