Simplifying a Radical by Factoring the Radicand
Simplifying a radical by factoring the radicand is demonstrated. The goal of simplifying a radical is to make an expression easier to deal with by getting the smallest number possible under the radical sign.
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: Finding Volume
A practical problem about volume is solved using division of a rational expression.
Approximate Square Roots
Finding the approximate square root for numbers that are not perfect squares is demonstrated. Irrational numbers are explained.
Approximating the Value of a Solution
Sometimes it makes sense to approximate the value of a solution. An example is given and the solution found.
Denominator of a Simplified Expression Never Has Radicals, The
A guideline is presented: a simplified radical expression never has radicals in the denominator. An expression with a radical in the denominator, but not in the numerator, is simplified using the identity property of multiplication and the process o...
Estimating Radicals to Set a Safe Speed Limit
A practical problem involving setting a speed limit is solved that involves estimating radicals to find the value of an irrational solution.
Multiplying then Simplifying Two Radicals
The procedure for simplifying radicals by beginning with multiplication is demonstrated.