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Introduction to Squares and Cubes

Learn about squares and cube numbers, including how to find the square and cube of a number, perfect squares and cubes, finding square roots, and estimating square roots. Practice exercises and homework included.

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Introduction to Squares and Cubes

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  1. Square and Square Roots; Cubes and Cube Roots Lesson 1

  2. Squares • The square of a number can be found by multiplying that number by itself. • Square the number 3: 3x3=9 • Since the number 3 is multiplied twice, it is written 32.

  3. Why call it “Squared?” • We call it squaring from the shape! • A square is unique because all 4 sides are the same, so length and width are the same number. • When we find the area, we are really multiplying a number by itself! • Area: Area= 3x3 or 32 3 3

  4. Cube • Multiply that number by itself 3 times. • Cube the number 6: 6x6x6 • It would be written 63 • Why cubed? Same idea as squared! • All sides of a cube are the same, so when we find the volume, we multiply the same number 3 times. • Volume: Volume= 3x3x3 or 33 3 3 3

  5. Perfect squares and Perfect cubes • Lets list all the perfect squares from 1-100: 1, 4, 9, 16, 25, 36, 49, 64, 81, 100 (12,22,32, 42, 52, 62, 72, 82, 92, 102) • Lets list all the perfect cubes from 1-125! 1, 8, 27, 64, 125 (13, 23, 33, 43, 53) • What number is both a perfect square and cube?

  6. Any questions so far?

  7. Square root • This is the inverse, or opposite, or squaring a number. • 32= 9 so √9 = 3 • A perfect square has a square root that is a whole number. • 9 is a perfect square because its square root is a whole number, 3. • 10 is not a perfect square because its square root is about 3.16, which is NOT a whole number.

  8. Finding Square Root • What is the √16? • Think back to those perfect squares… what number squared is 16? 4! So… √16= 4 • What is the √81? • What is the √36? • What is the 3√27?

  9. Practice • Let's practice what we just learned: - What is the value of 5 cubed? - What is the value of 2 squared? - What is the √16? - What is the √25? - What is the 3√64? - What number is a perfect square and a perfect cube? Show how you know.

  10. Taking it a step further • What about those numbers that are not perfect squares? √17 for example?! • Lets go back to that list of perfect squares… what perfect squares is close to 17? • So we can estimate the √17 to be between 4 and 5. • Let’s practice! • Estimate the square root of… √17, √40, √72, √23

  11. And your homework is…

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