1. Martin-Gay, Developmental Mathematics 1 Square Roots Opposite of squaring a number is taking the square root of a number. A number b is a square root of a number a if b 2 = a. In order to find a square root of a, you need a # that, when squared, equals a.

2. Martin-Gay, Developmental Mathematics 2 The principal (positive) square root is noted as The negative square root is noted as Principal Square Roots

3. Martin-Gay, Developmental Mathematics 3 Radical expression is an expression containing a radical sign. Radicand is the expression under a radical sign. Note that if the radicand of a square root is a negative number, the radical is NOT a real number. Radicands

4. Martin-Gay, Developmental Mathematics 4 Radicands Example

5. Martin-Gay, Developmental Mathematics 5 Square roots of perfect square radicands simplify to rational numbers (numbers that can be written as a quotient of integers). Square roots of numbers that are not perfect squares (like 7, 10, etc.) are irrational numbers. IF REQUESTED, you can find a decimal approximation for these irrational numbers. Otherwise, leave them in radical form. Perfect Squares

6. Martin-Gay, Developmental Mathematics 6 If and are real numbers, Product Rule for Radicals

7. Martin-Gay, Developmental Mathematics 7 Simplify the following radical expressions. No perfect square factor, so the radical is already simplified. Simplifying Radicals Example

8. Martin-Gay, Developmental Mathematics 8 Sums and Differences Rules in the previous section allowed us to split radicals that had a radicand which was a product or a quotient. We can NOT split sums or differences.

9. Martin-Gay, Developmental Mathematics 9 These are terms with the same variables raised to the same powers. They can be combined through addition and subtraction. Similarly, we can work with the concept of “like” radicals to combine radicals with the same radicand. Like radicals are radicals with the same index and the same radicand. Like radicals can also be combined with addition or subtraction by using the distributive property. Like Radicals

10. Martin-Gay, Developmental Mathematics 10 Can not simplify Adding and Subtracting Radical Expressions Example

11. Martin-Gay, Developmental Mathematics 11 Simplify the following radical expression. Example Adding and Subtracting Radical Expressions

12. Martin-Gay, Developmental Mathematics 12 If and are real numbers, Multiplying and Dividing Radical Expressions