Inverse operations w/equations using exponents and square

roots notes

Absent copy

Friday 5/9

Review of 2 step equations 2x -32 – 4 = 15

A) Add the oppisiteB) Combine like termsC) Inverse operation (sub. 5 from both sides)D) Inverse Operation (divide 2 on both sides)

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: x2 inverse is 2

2 = x · x = x2. 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

x

x

9 99 9 9

Example 1• Solve and Check (principal

root

y2 = 25

2 =

y · y = 5 · 5 y = 5

52 = 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

y 25

Example 2• Solve and check (principal

root)

x3 = 343

3 =

x · x ·x = 7 · 7 · 7 x = 7 73 = 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

3 x 343

Example 3• Solve and check (principal

root)

-7 + c2 = 189 +7 +7 0 + c2 = 196 c2 = 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 14C = 14

c 196

Example 4• Solve and check

(principal root). -10 + 33 = 1 + h2 -10 + 27 = 1 + h2 17 = 1 + h2 -1 = -1 + h2 16 = 0 + h2 16 = h2 = 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 4H = 4

16 h