Warm Up Simplify. 1. 52 2. 82 3. 122 4. 152 5. 202.

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Presentation transcript:

Warm Up Simplify. 1. 52 2. 82 3. 122 4. 152 5. 202

Think about the relationship between the area of a square and the length of one of its sides. area = 36 square units side length = 6 units because 62= 36 A number that when multiplied by itself to form a product is the square root of that product. Taking the square root of a number is the inverse of squaring the number. 62 = 36 36 = 6

Every positive number has two square roots, one positive and one negative. The radical symbol indicates the nonnegative or principal square root. The symbol – is used to indicate the negative square root. 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. –49 is not the same as – 49. A negative number has no real square root. Caution!

Additional Example: 1 Finding the Positive and Negative Square Roots of a Number Find the two square roots of each number. A. 49 B. 100 C. 225

A. 81 B. 144 C. 324 Check It Out: Example 1 Find the two square roots of each number. A. 81 9 • 9 = 81 81 = (–9)(–9) = 81 = ±9 B. 144 12 • 12 = 144 144 = (–12)(–12) = 144 = ±12 C. 324 18 • 18 = 324 324 = (–18)(–18) = 324 = ±18

Additional Example 2: Application A square window has an area of 169 square inches. How wide is the window? Write and solve an equation to find the area of the window. 132 = 169 So 169 = 13. Use the positive square root; a negative length has no meaning. The window is 13 inches wide. The area of a square is s2, where s is the length of a side. Remember!

Check It Out: Example 2 A square window has an area of 225 square inches. How wide is the window?

Additional Example 3A: Evaluating Expressions Involving Square Roots Simplify the expression. 3 36 + 7

Additional Example 3B: Evaluating Expressions Involving Square Roots Simplify the expression. 25 16 3 4 +

Check It Out: Example 3A Simplify each expression. 2 121 + 9 = 31 = 22 + 9 2 121 + 9 = 2(11) + 9

Check It Out: Example 3B Simplify each expression. 16 36 2 3 +

Check It Out: Example 3C Simplify each expression. –5 336 + 25