10/29/12 Unit 2Triangles Right Triangles I can….. simplify radical expressions.

Slides:

Advertisements

Similar presentations

Advertisements

Warm up Simplify

Simplifying, Multiplying, & Rationalizing Radicals

Simplifying Radicals. Perfect Squares Perfect Cubes

Simplifying Radicals you solve them? Topic: Radical Expressions

Aim: How do we simplify radical expressions? Do Now: List at least 3 factors of: x 4.

9.3 Simplifying Radicals.

12.5 Simplifying Square Roots CORD Math Mrs. Spitz Spring 2007.

Objectives The student will be able to:

Introduction to Radicals If b 2 = a, then b is a square root of a. MeaningPositive Square Root Negative Square Root The positive and negative square.

Simplifying Radicals.

Real Numbers Real Numbers are all numbers that can be located on Real Number line. This includes all whole numbers, all fractions, all decimals, all roots,

11.3 Simplifying Radicals Simplifying Radical Expressions.

DO NOW: SOLVE THE INEQUALITY BY FOLLOWING THE STEPS WE HAVE LEARNED OVER THE LAST TWO DAYS. THEN WE WILL GRAPH TOGETHER ON THE CALCULATOR;

Find square roots. Find cube roots. 7.1 Objective The student will be able to:

Objectives The student will be able to: 1. simplify square roots, and 2. simplify radical expressions. SOL: A.3 Designed by Skip Tyler, Varina High School.

Students will be able to estimate a square root, simplify a square root, and add and multiply square roots.

Objectives The student will be able to: 1. simplify square roots, and 2. simplify radical expressions.

Bell Ringer Use the Pythagorean Theorem to find the length of the hypotenuse.

Objectives The student will be able to: 1. simplify square roots, and 2.simplify radical expressions. Designed by Skip Tyler, Varina High School.

Lesson 10-1 Warm-Up.

The problem with this country is all the unsimplified radicals running around!!

Introduction to Irrational Numbers We write “irrational numbers” using a “radical symbol,” often just referred to as a “radical.” √ 3 is an irrational.

Radical The whole equation is called the radical. C is the radicand, this must be the same as the other radicand to be able to add and subtract.

Bell Ringer Use the Pythagorean Theorem to find the length of the hypotenuse.

Simplifying Radicals Section 5.3. Radicals Definition Simplifying Adding/Subtracting Multiplying Dividing Rationalizing the denominator.

Simplifying Radicals. Radical Flashback Simplifying Radicals: 1.Find the greatest perfect square that goes into the radicand. 2.Take the square root of.

Multiplying and Simplifying Radicals The Product Rule for Radicals is given by: Note that both of the radicals on the left have the same index. Throughout.

Simplifying Radicals. Perfect Squares

SWBAT…simplify radicals using the product property of radicalsWed, 3/14 Agenda 1. WU (10 min) 2. Lesson on product property of radicals – 13 examples!

Multiplying and Dividing Radicals The product and quotient properties of square roots can be used to multiply and divide radicals, because: and. Example.

11-1 Simplifying Radicals

SIMPLIFYING RADICAL EXPRESSIONS

To divide radicals: divide the coefficients divide the radicands if possible rationalize the denominator so that no radical remains in the denominator.

Warm Up Find each quotient / divided by 3/5

Radicals (Square Roots). = 11 = 4 = 5 = 10 = 12 = 6 = 7 = 8 = 9 = 2.

Simplifying Radicals Unit VIII, Lesson 4 Online Algebra

5-5 ROOTS OF REAL NUMBERS Objective: Students will be able to simplify radicals.

Simplifying Radicals Algebra I Unit 1 D2. Perfect Squares

HOW DO WE SIMPLIFY RADICALS? 1. simplify square roots, and 2. simplify radical expressions.

1.6 Objectives The student will be able to:

Warm-Up: HW #5: Simplifying radicals Agenda WU (10 min)

Multiplying & Dividing Radical Expressions

Simplifying Radicals Section 10-2 Part 1.

Objectives The student will be able to:

Simplifying Radical Expressions

Objectives The student will be able to:

Objectives The student will be able to:

Warm up Simplify

Objectives The student will be able to:

Simplifying Radicals.

Warm up Simplify

If x2 = y then x is a square root of y.

Simplifying Radicals.

Simplifying Radicals.

Objectives The student will be able to:

Adding & Subtracting Radical Expressions

5.2 Properties of Rational Exponents and Radicals

Simplifying Radicals.

Objectives The student will be able to:

Objectives The student will be able to:

Square Roots and Simplifying Radicals

Objectives The student will be able to:

9.3 Simplifying Radicals. Square Roots Opposite of squaring a number is taking the square root of a number. A number b is a square root of a number a.

Simplifying Radicals.

Objectives The student will be able to:

Dividing Radical Expressions

Objectives The student will be able to:

Objectives The student will be able to:

Presentation transcript:

10/29/12 Unit 2Triangles Right Triangles I can….. simplify radical expressions.

In the expression, is the radical sign and 64 is the radicand. 1. Find the square root: 8

2. Find the square root: 11, Find the square root: 21 4.Find the square root:

How do you know when a radical problem is done? 1. No radicals can be simplified. Example: 2. There are no fractions in the radical. Example: 3. There are no radicals in the denominator. Example:

6. Use a calculator to find each square root. Round the decimal answer to the nearest hundredth. 6.82, -6.82

Perfect Squares … 289

What numbers are perfect squares? 1 1 = = = = = = 36 49, 64, 81, 100, 121, 144,...

= = = = = = = = = = Perfect Square Factor * Other Factor LEAVE IN RADICAL FORM

Simplify

1. Simplify Find a perfect square that goes into 147.

2. Simplify Find a perfect square that goes into 605.

How do you simplify variables in the radical? Look at these examples and try to find the pattern… What is the answer to ? As a general rule, divide the exponent by two. The remainder stays in the radical.

4. Simplify Find a perfect square that goes into Simplify

Simplify 1. 3x x x x 18

6. Simplify Multiply the radicals.

7. Simplify Multiply the coefficients and radicals.

Simplify

8. Simplify. Divide the radicals. Uh oh… There is a radical in the denominator! Whew! It simplified!

9. Simplify Uh oh… Another radical in the denominator! Whew! It simplified again! I hope they all are like this!

10. Simplify Since the fraction doesn’t reduce, split the radical up. Uh oh… There is a fraction in the radical! How do I get rid of the radical in the denominator? Multiply by the “fancy one” to make the denominator a perfect square!