Simplifying Radicals NF.4.AC.2: Simplify, add, subtract and multiply radical expressions Students will learn to simplify radicals and to multiply and/or.

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Simplifying Radicals NF.4.AC.2: Simplify, add, subtract and multiply radical expressions Students will learn to simplify radicals and to multiply and/or divide radical expressions FHS Algebraic Connections

Algebraic Connections What is a factor? We say that we have factored 12 when we express 12 as the product of two or more integers (for example 12 = 3 • 4) We call 3 and 4 factors of 12. Let’s name some factors of 24: 2 and 12 3 and 8 6 and 4 FHS Algebraic Connections

Algebraic Connections What is a prime number? A prime number is a number whose only factors are itself and 1. 2, 3, 5, 7, etc. are examples of prime numbers. Let’s see if we can name 4 more prime numbers: All numbers that are not prime, we call composite numbers. They are made up of prime factors. To find all the prime factors, we will use prime factorization. 11 13 17 19 FHS Algebraic Connections

Algebraic Connections Prime Factorization To find the prime factorization, we will learn to use a factor tree. We start our factor tree with 24. Then we think of 2 factors of 24. Now 2 factors of 12 Now 2 factors of 6 Why don’t we find factors of 2 or 3? They are prime numbers. So, the prime factorization of 24 is 2 ∙ 2 ∙ 2 ∙ 3 = 23 ∙ 3 24 2 12 2 6 2 3 FHS Algebraic Connections

Algebraic Connections What is a radical? The square root of a number is written using the symbol and is called a radical. The number written inside this symbol is called the radicand. We need to simplify any radical that has a perfect square (a number with a whole number square root) as a factor of the radicand. We use prime factorization to help with simplifying the radical. FHS Algebraic Connections

Algebraic Connections Simplifying Radicals The steps for simplifying a radical are as follows: Use a factor tree to find the prime factorization. Circle any pair of numbers. Put one of each of the pairs of circled numbers outside the radical sign. All numbers not circled go inside the radical sign. Simplify the outside and inside of the radical. FHS Algebraic Connections

Algebraic Connections Simplifying a Radical To simplify this radical Find the prime factorization of 45. Circle any pair of identical numbers. The circled number goes outside the radical sign. The uncircled number goes inside the radical sign. 45 5 9 3 3 5 FHS Algebraic Connections

Algebraic Connections Simplifying a Radical To simplify this radical Find the prime factorization of 90. Circle any pair of identical numbers. The circled number goes outside the radical sign. The uncircled numbers go inside the radical sign. 90 9 10 3 3 2 5 3 2 · 5 FHS Algebraic Connections

Simplify These Radicals 1. 2. 3. 4. FHS Algebraic Connections