Math humor: Why wouldn’t the tree fit in the round pot? It had square roots.

1. Math humor: Why wouldn’t the tree fit in the round pot? It had square roots.

2. 3 Area = 32 3 Because the area of a square can be expressed using an exponent of 2, a number with an exponent of 2 is said to be squared. You read 32 as “three squared.” The square root of a number is one of the two equal factors of that number. Squaring a nonnegative number and finding the square root of that number are inverse operations.

3. Positive real numbers have two square roots, one positive and one negative. The positive square root, or principle square root, is represented by . The negative square root is represented by - .

4. A perfect square is a number whose square roots are integers.{you should memorize the perfect squares below} The first 11 perfect squares are below in the table.

5. Writing Math You can write the square roots of 16 as ±4, which is read as “plus or minus four.”

6. 49 = 7 49 = –7 – 100 = 10 100 = –10 – Example: Find the two square roots of each number. 1A. 49 7 is a square root, since 7 • 7 = 49. –7 is also a square root, since –7 • (–7) = 49. ±7 1B. 100 10 is a square root, since 10 • 10 = 100. –10 is also a square root, since –10 • (–10) = 100. ±10

7. 144c2 = (12c)2 z6 = (z3)2 Examples: Simplify the expression. 2A. 144c2 Write the monomial as a square. = 12|c| Use the absolute-value symbol. 2B. z6 Write the monomial as a square: z6 = (z3)2 = |z3| Use the absolute-value symbol.

8. 100n4 = (10n2)2 2C. 100n4 Write the monomial as a square. 10n2 is nonnegative for all values of n. The absolute-value symbol is not needed. = 10n2

9. So 169 = 13. Talking Example: Application A square window has an area of 169 square inches. How wide is the window? Find the square root of 169 to find the width of the window. Use the positive square root; a negative length has no meaning. 132 = 169 The window is 13 inches wide.