Squares, Roots, and Pythagorean Theorem

1. Squares, Roots, and Pythagorean Theorem 8th Grade Math December 2013-January 2014

2. Squares and Roots • Properties of Squares: • Side lengths: All the same • Area: b x h or side x side • Another way to write it: s2 • How can we find the side length of a square when all we know is the area? Area of 100 = 10 x 10; Area of 25 = 5 x 5; Area of 64 = 8 x 8. • We can write this mathematically using the radical symbol √ √100 = 10; √25 = 5; √64 = 8 • How do we say this? “The square root of 100 is 10; the square root of 25 is 5, the square root of 64 is 8….” Conclusions: The side length of a square is the root of the square!

3. More about squares and square roots • Identify the following perfect squares: √144 = 12 √121 = 11 √100 = 10 √81 = 9 √64 = 8 √49 =7 √36 = 6 √25 =5 √16 = 4 √9= 3 √4 = 2 √1 = 1 • How many patterns can you find? • We know that 42 = 16, and therefore, √16 = 4. This is called the principal square root because the root is an integer (a whole number). • Can you think of another integer multiplied by itself that has a product of 16? (-4)x(-4) = 16 √16 = 4 and -4. Conclusions: Every radical has two square roots, a positive and a negative.

4. Simplifying Expressions with square roots • Example 1: Find the two square roots of each number • √81 = +9, -9√1 = +1, -1√144 = +12, -12 • Example 2: A square computer icon contains 676 pixels. How many pixels tall is the icon? √676 = 26. Each side of the square computer icon is 26 pixels. Therefore, the square root of 676 is 26. • Example 3: Simplify each expression • 3√25 + 4 = √4 + ½ 3(5) + 4 = 2 + ½ = 2 ½ 15 + 4 = 19

5. REAL NUMBERS: