Warm-Up #5 Find the product of ab. Let a= 1 2 𝑎𝑛𝑑 𝑏= 25 36 . Simplify 91 Estimate: What is 17

Homework Advanced: Simplifying Radical Worksheet Page 1. #1-6 Page 2. #1-6 Regular: Simplifying Radical Worksheet Page 1. #1-4 Page 2. #1-4

Introduction to Radicals

Principal Square Roots The principal (positive) square root is noted as The negative square root is noted as

Perfect Squares 64 225 1 81 256 4 100 289 9 121 16 324 144 25 400 169 36 196 49 625

Simplify = 4 or -4 = 5 or -5 = 10 or -10 = 12 or -12

Simplify = = = = = = = = Perfect Square Factor * Other Factor LEAVE IN RADICAL FORM = = = =

Cube Roots The cube root of a real number a Example:

15.1 – Introduction to Radicals Cube Roots A cube root of any positive number is positive. A cube root of any negative number is negative. Examples:

Cube Roots Example

Simplifying Radicals

Product Rule for Radicals If and are real numbers,

Simplifying Radicals Example Simplify the following radical expressions. No perfect square factor, so the radical is already simplified.

Simplifying Radicals Example Simplify the following radical expressions.

Quotient Rule for Radicals If and are real numbers,

Simplifying Radicals Example Simplify the following radical expressions.

Adding and Subtracting Radicals

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.

Like Radicals What is combining “like terms”? Similarly, we can work with the concept of “like” radicals to combine radicals with the same radicand.

Adding and Subtracting Radical Expressions Example Can not simplify Can not simplify

Adding and Subtracting Radical Expressions Example Simplify the following radical expression.

Adding and Subtracting Radical Expressions Example Simplify the following radical expression.

Adding and Subtracting Radical Expressions Example Simplify the following radical expression. Assume that variables represent positive real numbers.

Multiplying and Dividing Radicals

Multiplying and Dividing Radical Expressions If and are real numbers,

Multiplying and Dividing Radical Expressions Example Simplify the following radical expressions.

Rationalizing the Denominator If we rewrite the expression so that there is no radical in the denominator, it is called rationalizing the denominator. Rationalizing the denominator is the process of eliminating the radical in the denominator.

Rationalizing the Denominator Example Rationalize the denominator.

Conjugates Many rational quotients have a sum or difference of terms in a denominator, rather than a single radical. need to multiply by the conjugate of the denominator The conjugate uses the same terms, but the opposite operation (+ or ).

Rationalizing the Denominator Example Rationalize the denominator.