Chapter 9 Section 3 Adding, Subtracting and Multiplying Square Roots

Learning Objective 1.Add and subtract square roots 2.Multiply square roots

Key Vocabulary like square roots unlike square roots product rule for square roots

Add and Subtract Square Roots Like square roots are square roots having the same radicands. They are added in the same way as other like terms. – Adding the coefficient is an application of the distributive property – Multiply the sum by the like square root Adding like terms 5x + 4x = (5 + 4)x = 9x Example:Example:Example: 7 = x = 3x + 4x 7 = 77x = (3 + 4)x 7x = 7x

Example: Add and Subtract Square Roots

Example: Add and Subtract Square Roots

Example: Add and Subtract Square Roots

Example: Add and Subtract Square Roots

Unlike square roots have different radicands. If possible change the unlike term to a like term Sometimes we can combine by simplifying first. Example: Add and Subtract Unlike Square Roots

Example: Add and Subtract Unlike Square Roots

Example: Add and Subtract Unlike Square Roots Example:

Add and Subtract Unlike Square Roots

Example: Add and Subtract Unlike Square Roots

When multiplying square roots we need to use the distributive property. x (x + 2) = x 2 + 2x Example: Multiplying Square Roots

Example:

Example: Multiplying Square Roots

When multiplying binomials with square roots. Each term in the first binomial is multiplied by each term in the second binomial. (FOIL) Example: Multiplying Square Roots

Example: Multiplying Square Roots Example:

Multiplying Square Roots

Example: Multiplying Square Roots

Difference in Two Squares: Example: OR Multiplying Square Roots

Example: OR Multiplying Square Roots

Example:

Remember Like square roots are square roots having the same radicands they are added in the same way as other like terms It may be helpful for you to review combining like terms from Chapter 2 Section 1. – Determine which terms are alike – Add or Subtract the coefficient of the like terms – Multiply the coefficient by the variable. Make sure you add or subtract the coefficient not multiplying them

Remember When multiplying square roots we need to use the distributive property When multiplying binomials with square roots. Each term in the first binomial is multiplied by each term in the second binomial. (FOIL)

HOMEWORK 9.3 Page : # 5, 9, 13, 19, 27, 37, 53, 61, 71, 79