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Understanding Squares & Square Roots: Learning and Practice Guide

Master identifying perfect and non-perfect squares, calculate square roots accurately, and estimate values between squares. Practice problems included for clarity.

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Understanding Squares & Square Roots: Learning and Practice Guide

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  1. SQUARES & SQUARE ROOTS

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

  3. 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

  4. Square Roots The Square Root of a number is the number you can multiply by itself to give you that number. Thus, = 2,because22=4 = 3,because32=9 Try: = 8, because 82=64 = 12,because122=144 =1, because 12 = 1 =0, because 02 = 0

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

  6. 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…

  7. 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

  8. 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

  9. 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?

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

  11. 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?

  12. 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?

  13. 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

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