Operations w/ Radicals Chapter 10, Section 3

Targets I will be able to simplify sums and differences of radical expressions. I will be able to simplify products and quotients of radical expressions.

Simplify sums & differences of radical expressions We use the distributive property to combine like terms. Ex) 5x + 4x = (5 + 4)x = 9x We will use this same principle to combine like radicals. Sometimes, you will need to simplify the radical expression to see if you have like radicals

Simplify = (4 + 1) 3Use the Distributive Property to combine like radicals. = 5 3Simplify = Both terms contain 3.

8 5 – 45 = is a perfect square and a factor of 45. Simplify 8 5 – 45. = 8 5 – 9 5Use the Multiplication Property of Square Roots. = 8 5 – 3 5Simplify 9. = (8 – 3) 5Use the Distributive Property to combine like terms. = 5 5Simplify. 10-3

You Try Got It, Prb 1, pg 613 Got It, Prb 2, pg 614

Simplify products of radical expressions Use distributive property or FOIL to multiply (or use the Punnett Square model).

Simplify 5( 8 + 9). 5( 8 + 9) = Use the Distributive Property. = Use the Multiplication Property of Square Roots. = Simplify. 10-3

You Try Got It, Prb 3, pg 614

Simplify quotients of radical expressions To rationalize the denominator in a radical expression (i.e. remove the radicals in the denominator), we multiply numerator & denominator by the conjugate of the denominator. Conjugates are the sum and difference of the same two terms. Example:

= 2( 7 + 3)Divide 8 and 4 by the common factor 4. = Simplify the expression. = Multiply in the denominator. 8( 7 + 3) 7 – 3 = Simplify the denominator. 8( 7 + 3) Simplify. 8 7 – 3 = Multiply the numerator and denominator by the conjugate of the denominator. 8 7 –

A painting has a length : width ratio approximately equal to the golden ratio (1 + 5 ) : 2. The length of the painting is 51 in. Find the exact width of the painting in simplest radical form. Then find the approximate width to the nearest inch Define:51 = length of painting x = width of painting Relate: (1 + 5) : 2 = length : width Write: = x (1 + 5) = 102Cross multiply. = Solve for x. 102 (1 + 5) x(1 + 5) (1 + 5) 51 x (1 + 5) 2

(continued) x = Multiply in the denominator. 102(1 – 5) 1 – 5 x =Simplify the denominator. 102(1 – 5) –4 x = Divide 102 and –4 by the common factor –2. – 51(1 – 5) 2 x = Use a calculator. x 32 The exact width of the painting is inches. The approximate width of the painting is 32 inches. – 51(1 – 5) x = Multiply the numerator and the denominator by the conjugate of the denominator. (1 – 5) 102 (1 + 5)

You Try Got Its, Prbs 4 & 5, pgs Lesson Check, prbs 1-8, pg 616