SQUARES & SQUARE ROOTS

Squares Square of a number: “Squaring” a number means to raise a number to the second power. Example: 4² = 4 · 4 = 16 9² = 9 · 9 = 81 16² = 16 · 16 = 256

Square Roots The Square Root of a number is the number you can multiply by itself to give you that number. Thus, = 2, because 22=4 = 3, because 32=9 Try: = 8, because 82=64 = 12, because 122=144 = 1, because 12 = 1 = 0, because 02 = 0

Perfect Squares A Perfect Square: is “perfect” because its square root is a whole number. Example: is a perfect square because = 49 7

Non-Perfect Squares A Non-Perfect Square: is a number whose square root is NOT a whole number. Example: is NOT a perfect square because = 40 6.3245…

Approximating Square Roots You need to estimate its value of non-perfect squares by determining which two perfect squares it falls in between. Example: 11 is a non-perfect square 11 falls between perfect squares 9 & 16 Therefore, is between and Since, = 3 and = 4 Then is between 3 and 4

Find the two consecutive numbers the following non-perfect square fall between. SHOW WORK! √55  √23 √5  √14 √44 and Between 7 & 8 and Between 4 & 5 and Between 2 & 3 and Between 3 & 4 and Between 6 & 7

Estimating Square Roots Not all numbers are perfect squares. Not every number has an Integer for a square root. We have to estimate square roots for numbers between perfect squares.

Estimating Square Roots To calculate the square root of a non-perfect square 1. Place the values of the adjacent perfect squares on a number line. 2. Interpolate between the points to estimate to the nearest tenth.

Estimating Square Roots Example: 27 What are the perfect squares on each side of 27? 25 30 35 36

Estimating Square Roots Example: 27 half 5 6 25 30 35 36 27 Estimate 27 = 5.2

Estimating Square Roots Example: 27 Estimate: 27 = 5.2 Check: (5.2) (5.2) = 27.04

Answer the following problem SHOW WORK! I am a number. I am not zero. If I am squared, I’m still the same number. What number am I? 1

Answer the following problem SHOW WORK! If a square bedroom has an area of 144 square feet, what is the length of one wall? 12 feet 14

Answer the following problem SHOW WORK! An artist is making two stained-glass windows. One window has a perimeter of 48 inches. The other window has an area of 110 inches. Which window is bigger? The window with a perimeter of 48 inches. 15

Answer the following problem SHOW WORK! A square garden has an area of 225 square feet. How much fencing will a gardener need to buy in order to place fencing around the garden? 60 feet 16

Homework Page 29, #8-13 Page 30 14-26