Secondary 2 lesson 2.4: Rational v Irrational, solve radical equations and equations with rational exponents.

Objective: By the end of the lesson you will be able to:

• Extend the properties of integer exponents to rational

exponents.

• Simplify expressions and determine if the answer is

rational or irrational.

• Solve simple equations that contain radical or rational

exponents.

Definitions: A RATIONAL number is a number that can be expressed as a fraction (or a ratio) of two integers. Examples:

An IRRATIONAL number CANNOT be expressed as a fraction. Irrational numbers can include non-repeating, non-terminating (never stops) decimals; square roots of non-perfect squares, etc........the most common 'look' of an irrational number is a number with a radical in it! Examples:

Example: Simplify each expression and decide if the answer is rational or irrational.

All the properties of powers can be applied to rational exponents. We just have to use the rules to add, subtract, and multiply fractions when we simplify. Remember the rules?

Multiplying Powers: Power of a Power: Power of a Product:

Quotient of Powers: Zero Exponents:

Negative Exponents:

Example: Simplify the expression. (The ½ is an exponent)

Is this number Rational or Irrational?

Example: Simplify the expression. (The ½ is an exponent)

New Material !

Now we want to look at solving equations that contain radicals or rational exponents. How would you solve ? or ?

To solve an equation with a radical:

1. Rewrite the radical in rational exponent form. 2. Raise both sides of the equation to the reciprocal of the rational exponent. 3. Simplify the rational exponent *then change to radical form. (Remember, it's usually easier if you find the root of the number before raising to the power.) *you do not always have to change back to radical form. See next example.

Are these numbers Rational or Irrational?

Watch how this is used.

Lesson 2.4 ~ Rational vs. Irrational Numbers (1.1.2), Solve simple equations with radical or rational exponents

Assignment:

Handout 2.4 (Review for extra credit)