SQUARES & SQUARE ROOTS

Learning Goal I can identify perfect squares and non- perfect squares I can estimate and calculate the square root of a whole number

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 the value of non-perfect squares by determining which two perfect squares they fall 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

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?

Answer the following problem SHOW WORK! If a square bedroom has an area of 144 square feet, what is the length of one wall? 10

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? 11

Answer the following problem SHOW WORK! A square garden has an area of 150 square feet. About how much fencing will a gardener need to buy in order to place fencing on one side of the garden? 12

Squares, Square Roots, & Prime Factorization A) Choose three different two-digit numbers. Determine the prime factorization of each number. B) Calculate the square of each number in part (a). Determine the prime factorization of each square. C) Compare the prime factorization of each square with the prime factorization of its square root. How can you use the prime factorization of a square to calculate its square root? D) Use the prime factorization of 23 409 to calculate its square root: 23 409 = 34 x 172