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Inverse operations w/equations using exponents and square roots notes Absent copy Friday 5/9

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Review of 2 step equations 2x -3 2 – 4 = 15 A) Add the oppisite B) Combine like terms C) Inverse operation (sub. 5 from both sides) D) Inverse Operation (divide 2 on both sides)

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Inverse Operations of exponents/square roots. 1. The inverse operation of exponents can be done by taking the square root. (This gets the variable by itself). What you do to one side you have to do to the other side of the = sign. Ex: x 2 inverse is 2 2 = x · x = x 2. The inverse operation of square roots can be done by squaring the term. What you do to one side you have to do to the other side of the = sign. Ex: inverse is ( ) 2 ( ) 2 = · = 3 · 3 = 9

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Example 1 Solve and Check (principal root y 2 = 25 2 = y · y = 5 · 5 y = 5 5 2 = 25 25 = 25 Solution Is “y” by itself? YES or NO How do I get “y” by itself? We use the inverse of exponents which is to take the square root. What is the rule we use when doing something on one side of the = sign? What we do to one side we have to do to the other side of the = sign. What 2 factors (the same) can we multiply to = the radicand? 5 and 5 What do we do last? We check the answer. Y = 5

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Example 2 Solve and check (principal root) x 3 = 343 3 = x · x ·x = 7 · 7 · 7 x = 7 7 3 = 343 343 = 343 Solution Is “x” by itself? YES or NO How do I get “x” by itself? We use the inverse opp. Of exponents and take the cubed root. What is the rule we use when doing something on one side of the = sign? What you do to one side you have to do to the other side of the = sign. What 3 factors (the same) can we multiply to = the radicand? 7 and 7 and 7 What do we do last? We check the solution. X = 7

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Example 3 Solve and check (principal root) -7 + c 2 = 189 +7 +7 0 + c 2 = 196 c 2 = 196 2 = c · c = 14 · 14 c = 14 Solution Is there any GEMA to do before using inverses? YES or NO What inverse opp. Do we using first? We use the inverse opp. of subtraction and we add 7 to both sides. What inverse opp. Do we using next? We use the inverse opp. Of exponents and we take the square root of both sides. What 2 factors (the same) can we multiply to = the radicand? 14 and 14 C = 14

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Example 4 Solve and check (principal root). -10 + 3 3 = 1 + h 2 -10 + 27 = 1 + h 2 17 = 1 + h 2 -1 = -1 + h 2 16 = 0 + h 2 16 = h 2 = 2 4 · 4 = h · h 4 = h Solution Is there any GEMA to do before using inverses? YES or NO What inverse opp. Do we using first? We use the inverse opp. Of addition and subtract 1 from both sides. What inverse opp. Do we using next? We use the inverse opp. Of exponents and take the square root on both sides. What 2 factors (the same) can we multiply to = the radicand? 4 and 4 H = 4

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