Square Roots Holt Algebra 1

Simplify each expression. 1. 62 2. 112 121 36 25 36 3. (–9)(–9) 81 4. Write each fraction as a decimal. 2 5 5 9 5. 0.4 6. 0.5 5 3 8 –1 5 6 7. 5.375 8. –1.83

A number that is multiplied by itself to form a product is called a square root of that product. The operations of squaring and finding a square root are inverse operations. The radical symbol , is used to represent square roots. Positive real numbers have two square roots. = 4 Positive square root of 16 4  4 = 42 = 16 (–4)(–4) = (–4)2 = 16 – = –4 Negative square root of 16

The nonnegative square root is represented by The nonnegative square root is represented by . The negative square root is represented by – . A perfect square is a number whose positive square root is a whole number. Some examples of perfect squares are shown in the table. 1 4 9 16 25 36 49 64 81 100 02 12 22 32 42 52 62 72 82 92 102

The expression does not represent a real number because there is no real number that can be multiplied by itself to form a product of –36. Reading Math

Example 1: Finding Square Roots of Perfect Squares Find each square root. A. Think: What number squared equals 16? 42 = 16 Positive square root positive 4. = 4 B. Think: What is the opposite of the square root of 9? 32 = 9 = –3 Negative square root negative 3.

Example 1C: Finding Square Roots of Perfect Squares Find the square root. Think: What number squared equals ? 25 81 Positive square root positive . 5 9

Check It Out! Example 1 Find the square root. 1a. 22 = 4 Think: What number squared equals 4? = 2 Positive square root positive 2. 1b. 52 = 25 Think: What is the opposite of the square root of 25? Negative square root negative 5.

The square roots of many numbers like , are not whole numbers The square roots of many numbers like , are not whole numbers. A calculator can approximate the value of as 3.872983346... Without a calculator, you can use square roots of perfect squares to help estimate the square roots of other numbers.

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 2: Simplifying Square–Root Expressions Simplify each expression. C. Product Property of Square Roots D. Quotient Property of Square Roots

Simplify each expression. Check It Out! Example 2 Simplify each expression. C. Product Property of Square Roots D. Quotient Property of Square Roots

Partner activity…. Choose one……

HOMEWORK: 12 problem worksheet