Find the Square Root: 1) 3) 2) 4) Warm-Up Find the Square Root: 1) 3) 2) 4)

Objectives Estimate square roots. Simplify square roots.

The side length of a square is the square root of its area The side length of a square is the square root of its area. This relationship is shown by a radical symbol . The number or expression under the radical symbol is called the radicand. The radical symbol indicates only the positive square root of a number, called the principal root. To indicate both the positive and negative square roots of a number, use the plus or minus sign (±). or –5

Example 1: Estimating Square Roots Estimate to the nearest tenth. Find the two perfect squares that 27 lies between. < 5 < < 6 Find the two integers that lies between . Because 27 is closer to 25 than to 36, is close to 5 than to 6. Try 5.2: 5.22 = 27.04 Too high, try 5.1. 5.12 = 26.01 Too low Because 27 is closer to 27.04 than 26.01, is closer to 5.2 than to 5.1. Check On a calculator ≈ 5.1961524 ≈ 5.2 rounded to the nearest tenth. 

Estimate to the nearest tenth. Check It Out! Example 1 Estimate to the nearest tenth. Find the two perfect squares that –55 lies between. < –7 < < –8 Find the two integers that lies between – . Because –55 is closer to –49 than to –64, is closer to –7 than to –8. Try 7.2: 7.22 = 51.84 Too low, try 7.4 7.42 = 54.76 Too low but very close Because 55 is closer to 54.76 than 51.84, is closer to 7.4 than to 7.2. Check On a calculator ≈ –7.4161984 ≈ –7.4 rounded to the nearest tenth. 

Numbers such as 25 that have integer square roots are called perfect squares. Square roots of integers that are not perfect squares are irrational numbers. You can estimate the value of these square roots by comparing them with perfect squares. For example, lies between and , so it lies between 2 and 3.

Square roots have special properties that help you simplify, multiply, and divide them.

Example 2: Simplifying Square–Root Expressions Simplify each expression. A. Find a perfect square factor of 32. Product Property of Square Roots B. Quotient Property of Square Roots

Simplify each expression. Check It Out! Example 2 Simplify each expression. A. Find a perfect square factor of 48. Product Property of Square Roots B. Quotient Property of Square Roots Simplify.

Example 3B: Rationalizing the Denominator Simplify the expression. Multiply by a form of 1.

Check It Out! Example 3a Simplify by rationalizing the denominator. Multiply by a form of 1.

Check It Out! Example 3b Simplify by rationalizing the denominator. Multiply by a form of 1.

Homework! Holt 1.3 p. 24 # 1-13, 18-33