Course Squares and Square Roots Warm Up Simplify

Course Squares and Square Roots Learn to find square roots. Course 3 4-5

Course Squares and Square Roots Vocabulary principal square root perfect square

Course Squares and Square Roots Think about the relationship between the area of a square and the length of one of its sides. Taking the square root of a number is the inverse of squaring the number. Every positive number has two square roots, one positive and one negative. One square root of 16 is 4, since 4 4 = 16. The other square root of 16 is –4, since (–4) (–4) is also 16. You can write the square roots of 16 as ±4, meaning “plus or minus” 4. area = 36 square units side length = 36 = 6 units 6 2 = = 6

Course Squares and Square Roots The numbers 16, 36, and 49 are examples of perfect squares. A perfect square is a number that has integers as its square roots. Other perfect squares include 1, 4, 9, 25, 64, and 81. When you press the key on a calculator, only the nonnegative square root appears. This is called the principal square root of the number = 4 – 16 = –4 –49 is not the same as – 49. A negative number has no real square root. Caution!

Course Squares and Square Roots Finding the Positive and Negative Square Roots of a Number Find the two square roots of each number.

Course Squares and Square Roots Example 1 7 is a square root, since 7 7 = 49. –7 is also a square root, since –7 –7 = is a square root, since = 100. –10 is also a square root, since –10 –10 = = –7 – 49 = = = –10 – A. 49 B. 100 C is a square root, since = = = –15 – –15 is also a square root, since –15 –15 = 225.

Course Squares and Square Roots A. 25 Example 2 5 is a square root, since 5 5 = 25. –5 is also a square root, since –5 –5 = is a square root, since = 144. –12 is also a square root, since –12 –12 = = –5 – 25 = = = –12 – B. 144 C = = –17 – 17 is a square root, since = 289. –17 is also a square root, since –17 –17 = 289.

Course Squares and Square Roots Perfect Square Roots: Daily Grade Memorize 1² = 1 2² = 4 3² = 9 4² = 16 5² = 25 6² = 36 7² = 49 8² = 64 9² = 81 10² = ² = ² = ² = ² = ² = ² = ² = ² = ² = ² = ² = ² = ² = ² = ² = ² = ² = ² = ² = ² = 900

Course Squares and Square Roots Evaluating Expressions Involving Square Roots Evaluate the expression.

Course Squares and Square Roots Example 4 Evaluate the square root. Add. = 25 Multiply. = = 3(6) + 7

Course Squares and Square Roots Example = Evaluate the square roots. = = = 2 Add.

Course Squares and Square Roots Example 6 Evaluate the square root. Add.= 14 Multiply.= = 2(5) + 4

Course Squares and Square Roots Example t = + 9 Evaluate the square roots. = t2 = 9. = 3 Add. 1414

Course Squares and Square Roots Lesson Summary Find the two square roots of each number Evaluate each expression – 2 49 99 Ms. Estefan wants to put a fence around 3 sides of a square garden that has an area of 225 ft 2. How much fencing does she need? 45 ft 6. Draw a Radicand 7. Draw a Radical 8. Define a Perfect Square