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Understanding Square Roots: Area vs Length of Squares

Explore the relationship between the area and side lengths of squares through geometric understanding of square roots. This investigation includes exact and approximate calculations for squares with areas of 12, 19, 50, and 64 square units. Discover how perfect squares relate to their side lengths, and why area is measured in square units due to the multiplication of two dimensions. Engage in practice problems to solidify your knowledge of these concepts. Enhance your mathematical skills while discovering interesting facts about the universe, such as the longest animal and the longest place name.

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Understanding Square Roots: Area vs Length of Squares

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  1. Welcome to math!Thursday, April 12 Objective of Investigation 2.3 Use geometric understanding of square roots to find lengths of the line segments on a dot grid.

  2. Area vs. Lengthof a s • What is the exact side length of the square? = √12 units • What is the approximate side length of the square? ≈ 3.464101615 units 12 units2

  3. Area vs. Lengthof a s • What is the exact side length of the square? = √19 units • What is the approximate side length of the square? ≈ 4.358898935 units 19 units2

  4. Area vs. Lengthof a s • What is the exact side length of the square? = √50 units • What is the approximate side length of the square? ≈ 7.071067811 units 50 units2

  5. Area vs. Lengthof a s • What is the exact side length of the square? = 8 units • Why is there no approximate side length of this square? Because 8 ∙ 8 = 64 64 is considered a perfect square 64 units2

  6. Can you think of any otherperfect squares? 49 1 4 25 16 36 9

  7. Area vs. Lengthof a s • What is the area of this square? = 5.29 units2 • Why does area’s unit measure squared? Because you are multiplying 2 dimensions, length x height 2.3 units ? units2

  8. Practice Do page 25 35 - 38

  9. Longest Day • Venus rotates so slowly its day length is longer than its year. At 243 days it is equivalent to almost eight Earth months.

  10. Longest animal in the world • The longest animal is the bootlace worm, Lineuslongissimus; it reaches lengths of 60 metres (that’s just under 200 feet).

  11. Longest place name in the world • Llanfairpwllgwyngyll-gogerychwyrndrobwll-llantysiliogogogoch is a large village and community on the island of Anglesey in Wales.

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