Bell Ringer Name all of the sets of numbers to which each real number belongs. Natural, Whole, Integer, Rational, Irrational #1. 4 #2. 3/5 #3. -7/2 #4. √26

Supply Check I have decided to announce the first supply check. This will happen on FRIDAY, OCTOBER 24 I will be looking for pencil, piece of paper, calculator, and red pen.

Continue 10. 1 and 10.2 Radicals and Real Numbers R drive > Key > Week 11 > Wednesday > Finish 10.1 and 10.2 File > Save As > P drive > math > Week Finish 10.1 and 10.2

Simplifying Radicals

Vocabulary Radical Expression – An expression that contains a square root Radicand – the expression under the radical sign

Notes Product Property of Square Roots: A radicand is in simplest form if it contains no perfect square factors other than 1. The following property can be used to simplify square roots. Product Property of Square Roots: For any numbers a and b, where a ≥ 0 and b ≥ 0, the square root of the product ab is equal to the product of each square root. Symbols: Example: The Product Property of Square Roots and prime factorization can be used to simplify radical expressions in which the radicand is not a perfect square.

Simplify Square Roots: Example 1) = step one: prime factorization of 12 step twp: product property of sq roots step three: simplify

Your turn: Remember the steps…… step one: prime factorization step two: product property of sq roots step three: simplify Example 2)

The product property can also be used to multiply square roots: Multiply Square Roots Example 3) Find

Your turn: remember the steps 2b)

A fraction containing radicals is in simplest form if 1) no prime factors appear under the radical sign with an exponent greater than 1 and if 2) no radicals are left in the denominator. Rationalizing the denominator of a radical expression is a method used to eliminate radicals from the denominator of a fraction.

Rationalizing the Denominator: 3a) Simplify step one: multiply by a fraction with the denominator of this fraction in its numerator and denominator. • = (I will explain) step two: simplify if necessary

Your turn: remember the steps 3b)

More Practice: Simplify: Write problems and show work on notebook paper. 1) 2) 3) 4) 5) 6) 7)

Example 3 Compare Real Numbers

Example 4 Compare Real Numbers

Your Turn Practice Comparing Real Numbers

Example 5 Order Real Numbers

Example 6 Order Real Numbers

Your Turn Practice Ordering Real Numbers

Example 7 Solve Equations

Example 8 Solve Equations Solve each equation. Round to the nearest tenth, if necessary. W2 = 169 R2 = 50

Your Turn Practice Solving Equations

Example 9 Use Real Numbers to Solve Problems

Example 10 Use Real Numbers to Solve Problems The formula for aspect ratio R is R = s2/A, where s is the wingspan in feet and A is the area of the wing. What is the wingspan of a hang glider if the aspect ratio is 6.4 and the area of the wing is 40 square feet?

Your Turn Practice Using Real Numbers to Solve Problems

Homework Section 10.1 #1-13

Homework Section 10.1 #1-13