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Applications of Squared Numbers and Square Root

Applications of Squared Numbers and Square Root. 7 th Grade Math September 9, 2013 Ms. DeFreese. Finding the Area. 8 units. To find the area of a square we multiply the length of a side times itself. For this square, 8 x 8 = 64. 8 x 8 = 8 2 = 64. 8 units.

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Applications of Squared Numbers and Square Root

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  1. Applications of Squared Numbers and Square Root 7th Grade Math September 9, 2013 Ms. DeFreese

  2. Finding the Area 8 units • To find the area of a square we multiply the length of a side times itself. • For this square, 8 x 8 = 64

  3. 8 x 8 = 82 = 64 8 units • Multiplying a number times itself is referred to as “squaring a number”. • This is written as n2, where n is the number that you are multiplying times itself. 64 squares total

  4. Perfect Squares • Any number raised to the power of 2 can be modeled using a square. That's why we call raising a number to the second power "squaring the number.” • The perfect squares are squares of whole numbers. • Here are the first five perfect squares.

  5. Finding the Side • You know that the area of a square is a number times itself, or n2. • We can find the length of the side of the square by finding out what n is. • This “working backwards” is called finding the square root. 64 squares total

  6. The square root of a number n is a number that, when multiplied by itself, equals n • For this square: 8 x 8 = 82 = 64 n = 8 So the square root of 64 is 8. This symbol for square root is √ So we write √64 = 8 64 squares total

  7. Example

  8. Arrays model n2and √n2

  9. Model for 72 = 49 Model for √49 = 7

  10. Model for √100 = 10 Model for 102 = 100

  11. Practice

  12. Are square roots really needed in life outside of math class? • any kind of job that deals with triangles; for example, it is needful for carpenters, engineers, architects, construction workers, those who measure and mark land, artists, and designers • “One time I observed people who needed to measure and mark on the ground where a building would go. Well, they had the sides marked, and they had a tape measure to measure the diagonals, and they asked ME what the measure should be, because they couldn't quite remember how to do it. This diagonal check is to ensure that the building is really going to be a rectangle and not a parallelogram. It is not easy to be sure that you have really drawn the two sides in a right angle.”

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