Benchmark: H.1.1.a. Extend the properties of exponents to rational exponents. H.1.1.a.ii. Rewrite expressions involving radicals and rational exponents.

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Presentation transcript:

Benchmark: H.1.1.a. Extend the properties of exponents to rational exponents. H.1.1.a.ii. Rewrite expressions involving radicals and rational exponents using the properties of exponents. Objectives:  find all the prime factors of a number  simplify radical expressions

Radicals  Because = 4 : 2 is a square root of 4  In the expression, the is the radical sign and 64 is the radicand.

Example1 Find the square root:

Practice1 Find the square root:

Perfect Squares List some perfect squares. 1 1= ____22 = ____33 = ____ 44 = _____ 55 = _____ 66 = ____ 77 = ____ 88 = _____ 99 = _____ 1010 = ______

The FANCY way to simplify a radical expression Simplify : Ugly Answer: ____________

The FANCY way to simplify a radical expression Simplify : Step 1: Find a perfect square that goes into 147.

The FANCY way to simplify a radical expression Simplify : Step 2: Split up the radical and simplify.

The EASY way to simplify a radical expression  Factoring is a way to find ALL the prime numbers that go into a number.  A prime number can only be divided by 1 and itself.

Example 2 Find all the prime factors of

Practice 2 Find all the prime factors of

The EASY way to simplify a radical expression  When simplifying a square root, the first step is to factor the number.  Only take 1 number from each pair outside of the radical.

Example 3: Use whiteboard to factor Simplify the following expression:

Example 3 Simplify the following expression:

Example 3 Simplify the following expression: DOUBLE CHECK!!

Practice 3 Simplify the following expression:

Practice 3 Simplify the following expression:

Practice 3 Simplify the following expression: DOUBLE CHECK!!

Example 4 Simplify the following expression:

Simplify the following expression: Example 4

Practice 4 Simplify the following expression:

Simplify the following expression: Practice 4

Example 5 Simplify the following expression:

Simplify the following expression: Example 5

Practice 5 Simplify the following expression:

Practice 5 Simplify the following expression:

Example 6 The formula can be used to find the size of a square sector where a is the area of the square and s is the length of a side. What is the length of the side of a square with an area of 729 sq. miles? 729 = a or s?

Whiteboards!!!

Find the square root:

Draw a factor tree for:

Simplify the following expression:

Draw a factor tree for:

Simplify the following expression: