Chapter 3: Real Numbers and the Coordinate Plane

Square Roots The square root of a number is another number that when multiplied by itself is equal to the original number I know, so the

Square Root If a number has a square root, it has two SO…

Square roots Remember: positive x positive = positive negative x negative = negative Therefore… This is not a real number! (It is imaginary, but we are not getting into that)

Perfect Squares When the square root comes out as a whole number it is a perfect square

Use Perfect Squares to Estimate Other Square Roots NOTE: This number is irrational, it can not be written as a fraction and will not stop or repeat, just like Pi. This is true for all non-perfect squares.

Rational Vs. Irrational Remember rational numbers can be written as a fraction – Repeating decimals – Integers (positive and negative whole numbers) – Fractions – Terminating decimals (the decimal stops) Irrational – Square roots that are not perfect squares – Decimals that don’t stop or repeat

Square roots in Algebra The square root is the opposite of squaring a number Just like division undoes multiplication, the square root will undo squaring a number Remember to do order of operations backwards (easy operations first)

Square Roots in Algebra Opposite of multiplying by 16 is dividing by 16 Calculate 816/16=51 Square root and squaring cancel out

Homework Page odd

The Pythagorean Theorem It is a formula! a b c NOTE: The hypotenuse is always the longest side, and the side opposite the right angle NOTE: this only works for right triangles

Using the Formula Just like every other formula, copy it down and list your variables 5cm 10cm c

Substitute into the Formula

Solve the Formula Don’t forget your units!

Homework Page

Pythagorean theorem with unknown Leg Variables (a) and (b) are interchangeable, But if you are given the hypotenuse and a leg, you need to find the other leg with algebra 9cm 3cm x Substitute into the formula

Solving with algebra Opposite of adding 9 is subtracting 9 Don’t forget units!

Tips Give yourself plenty of space to work Draw pictures to illustrate situations from word problems If the answer is not a perfect square, leave it under the radical sign ( )

Homework Page

Graphing in the Coordinate Plane Ordered Pairs: give the location of a point on my plane The first number is the x coordinate The second number is the y coordinate

Pythagorean theorem with the Coordinate Plane See notes on Pythagorean Theorem for details on solving

Homework Page

Equations, Tables, and Graphs All three can be used to represent the same data

Suppose you save three dollars a week Table: Number of weeks (x) Total savings (y)expression x

Suppose you save three dollars a week Table: Number of weeks (x) Total savings (y)Expression x

Suppose you save three dollars a week Table: Number of weeks (x) Total savings (y)Expression x

Suppose you save three dollars a week Table: Number of weeks (x) Total savings (y)Expression x

Suppose you save three dollars a week Table: Number of weeks (x) Total savings (y)Expression x

Suppose you save three dollars a week Table: Number of weeks (x) Total savings (y)Expression xy

Suppose you save three dollars a week Look for patterns. What do I do to one column to get the next? Number of weeks (x) Total savings (y)Expression xy Rule: Multiply by 3

Suppose you save three dollars a week Look for patterns. What do I do to one column to get the next? Number of weeks (x) Total savings (y)Expression 003(0) 133(3) 263(2) 393(3) 4123(4) xy3(x) Rule: Multiply by 3

Graph It Number of weeks (x) Total savings (y) ExpressionOrdered Pair 003(0)(0,0) 133(3)(1,3) 263(2)(2,6) 393(3)(3,9) 4123(4)(4,12) xy3(x)(x,y) Plot these points on the coordinate plan and connect the dots with a straight line.

For lines you only need 2 points

Homework Page