Practical Problem: Skid Marks and Speeding Cars
A practical application for using an approximate square root is illustrated in finding the speed a car was travelling before an accident occurred.
Simplifying Radicals Using Multiplication
Radicals are simplified using multiplication, illustrating when to multiply first and then find the square root of the product and when to find the square root first and then multiply.
Simplifying Radicals With Variables
Using the rules for simplifying radicals with numbers in the radicand to simplify radicals with variables.
Rationalizing the Denominator with Variables in the Radicand
Rationalizing the denominator with a variable in the radical is demonstrated.
Practical Problem: Where to Place the Braces
The Pythagorean Theorem is used to calculate where the braces should be placed to hang a store's sign so that the bottom falls six inches above the door.
Factoring Quadratic Equations Review
Two methods of solving quadratic equations are factoring and finding the square root on each side; reviewed here.
Solve: 9x2 - 24x = -16
Practice solving an equation using the quadratic formula: 9x2 - 24x = -16.
Finding the Length of the Third Side of a Right Triangle
The Pythagorean Theorem can also be used to determine the length of the hypotenuse given the length of the legs, or the length of a leg given the length of the hypotenuse and the other leg. The formula is demonstrated for both purposes.
Practical Problem: Diameter of a Log
The Pythagorean Theorem can be used to find the diameter of a circle. A practical problem involves finding the smallest log that can be cut to yield a square beam of a given size.
Rewriting Radical Notation Using Rational Exponent Form
Finding the value of a radical by writing it in rational exponent form.