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Simplifying Radicals

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. What is a factor?.

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Simplifying Radicals

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  1. 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 Algebraic Connections

  2. What is a factor? • We say that we have factored12 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 Algebraic Connections

  3. What is a prime number? • A prime number is a number whose onlyfactors 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 Algebraic Connections

  4. 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 Algebraic Connections

  5. 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. Algebraic Connections

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

  7. 45 5 9 3 3 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. 5 3 Algebraic Connections

  8. 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 3 325 3 2 · 5 Algebraic Connections

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

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