Lesson 39 Sections 7.5 and 7.6When two radicals have the same indices and same radicands, they are said to be 'like radicals'. They can be combined the same as 'like terms'.Like Radicals: rrr 4 , ,3 333512 ,53 ,52 mmxm 44452 ,510 ,55 Unlike Radicals: 32 ,4 xx33310 ,5 ,4Add like terms: yxyxyx 98121032 Add like radicals: 33349284122104322 Simplify by combining 'like radicals'.1)3337578772) 2103837253) 323433933Sometimes radicals must be simplified before combining.4) 845095) xx 123436)335458127) 181284323985Multiply the following radicals: )523)(842()58)(24)(32( ----1Remember that the product rule for radicals says radicands can be multiplied as long as the indices are the same.3064Multiply using either the distributive property or FOIL.8) )532(59) )3262(310) )52)(54(11) )235)(272(12)2)63(13)2)23( xThe following binomials are called conjugates. With conjugates only do the F and L of FOIL.14) )342)(342(15) )35)(35(23xYou know you can add, subtract, multiply, or divide (by nonnegative number) andget a true equation. Let's see if both sides can be raised to the same power. Square both sides.92xIs x = 3 still a solution? Yes. However, 3 could also be a solution of the squared equation. So raising both sides to the same power results in an equation with a solution of the original equation. However, sometimes there may also be solutions that are not solutions of the original equation. Power Rule: If ba , then 22ba has the same solution as the original equation. However, the squared equation may also have 'extra' solutions that are not solutions of the original equation. Therefore, all solutions of a squared equation must be checked in the original equation.Solve the following equations. Check all solutions.16)623 xBefore squaring, the radical must be isolated.17)52 x18)751 a19)472
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