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Understanding Roots and Radicals in Mathematics

This lesson covers finding square roots and n-th roots of numbers, distinguishing between positive and negative square roots, understanding radicals, and exploring the properties of roots. Students will learn about the principles of square roots, n-th roots, and how to determine the domain of a root. The lesson includes examples and activities to reinforce learning.

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Understanding Roots and Radicals in Mathematics

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  1. Lesson 7-1:Radical Expressions Objectives Students will: Find square roots of numbers Find n-th root of numbers

  2. Square Root The square root of a is c if c2 = a → if There are 2 square roots of positive numbers: c2 = a and (-c)2 = a Example 1 Find the square roots of each: 49 225 Principle Square Root : ,when the positive square root is wanted Negative Square Root: ,when the negative square root is wanted

  3. Radicals: is called a radicalsign Any expression with this sign is a radical expression The expression under the is the radicand Radical Property The square root of a perfect square is the absolute value of the value being squared (principle square root) Example 2

  4. N-th Roots means c3 = a → c is the “cube root” Can have 4th roots, 5th roots,…. is the n-th root of a number Activity - Find the following: Is there a pattern with the answers and the n-value?

  5. N-th Root Property , when n is even (always +) , when n is odd (can be + or -) , does not exist when n is even Determine domain of a root.

  6. Examples: • Give the roots of 169 • Simplify • Simplify • Simplify • Simplify • 8) Find domain:

  7. assignment 7-1/295-296/ 2-64e

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