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Operations w/ Radicals

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.

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Operations w/ Radicals

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  1. Operations w/ Radicals Chapter 10, Section 3

  2. 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.

  3. 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

  4. Simplify 4 3 + 3. 4 3 + 3 = 4 3 + 1 3 Both terms contain 3. = (4 + 1) 3 Use the Distributive Property to combine like radicals. = 5 3 Simplify. 10-3

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

  6. You Try • Got It, Prb 1, pg 613 • Got It, Prb 2, pg 614

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

  8. Simplify 5( 8 + 9). 5( 8 + 9) = 40 + 9 5 Use the Distributive Property. = 4 • 10 + 9 5 Use the Multiplication Property of Square Roots. = 2 10 + 9 5 Simplify. 10-3

  9. You Try • Got It, Prb 3, pg 614

  10. Simplify quotients of radical expressions • To rationalizethedenominator 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:

  11. 8 7 – 3 Simplify . 8 7 – 3 7 + 3 7 + 3 = • Multiply the numerator and denominator by the conjugate of the denominator. 8( 7 + 3) 7 – 3 8( 7 + 3) 4 = Multiply in the denominator. = Simplify the denominator. = 2( 7 + 3) Divide 8 and 4 by the common factor 4. = 2 7 + 2 3 Simplify the expression. 10-3

  12. Define: 51 = length of painting x = width of painting Relate: (1 + 5) : 2 = length : width (1 + 5) 2 Write: = x (1 + 5) = 102 Cross multiply. = Solve for x. 51 x 102 (1 + 5) x(1 + 5) (1 + 5) 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. 10-3

  13. 102 (1 + 5) (1 – 5) (1 – 5) x = • Multiply the numerator and the denominator by the conjugate of the denominator. 102(1 – 5) 1 – 5 x = Multiply in the denominator. 102(1 – 5) –4 x = Simplify the denominator. – 51(1 – 5) 2 – 51(1 – 5) 2 x = Divide 102 and –4 by the common factor –2. x = 31.51973343Use a calculator. x 32 The exact width of the painting is inches. The approximate width of the painting is 32 inches. (continued) 10-3

  14. You Try • Got Its, Prbs 4 & 5, pgs 615-616 • Lesson Check, prbs 1-8, pg 616

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