Rational vs. Irrational Numbers: In the last unit you worked with quadratics with rational solutions (x-intercepts). We will now go into quadratics with irrational and imaginary solutions.
Watch the video lined below then complete the skill.
Watch the video lined below then complete the skill.
Simplifying Radicals: Before we begin finding solutions that are irrational we need to practice simplifying radicals. A radical is only simplified if there are no perfect square factors under the radical. Watch the video that is posted and take notes. Then complete the practice skill.
Rationalizing the Denominator: A radical is not simplified if there is a radical in the denominator. The process of removing the radical from the denominator without changing its value is called rationalizing the denominator. Watch the video linked below then complete the practice skill.
Adding and Subtracting Radicals: In order to add or subtract radicals, they must be like radicals. For example: 5√2 - 2√2 = 3√2. This process is very similar to combining like terms. Always simplify radicals first to identify if they are like radicals.
Watch the video below then complete the practice skill.
Watch the video below then complete the practice skill.
Multiplying Radical Expressions: To multiply rational expressions, just multiply coefficients (outside numbers), multiply the radicands (inside numbers) then simplify. You will also be using the distributive property. Watch each of the example videos then complete the practice skill.