Radicals Whose Radicands are Perfect Squares
A radical and its parts are explained and the procedure for simplifying a radical whose radicand is a perfect square is illustrated. A practical application for this skill is presented.
Negative Exponents in the Denominator
Simplifying an expression with a negative exponent in the denominator, and a formula that makes it easier.
Practical Problem: How Much Land to Buy
A practical problem involving the purchase of land is presented. The available information is organized into a table, an equation is written, then solved using the least common denominator to get a quadratic equation, and the solution checked.
Simplifying the Square Root of Larger Numbers
Simplifying the square root of a larger number.
Roots Other Than Square Roots
Simplifying radicals with cube roots and other roots.
Solving a Quadratic Equation Using the Quadratic Formula
Quadratic equations that cannot be solved by factoring or the square root method can be solved using the quadratic formula. When an equation is in standard form, the values of a, b, and c, including their signs, can be substituted for the letters in...
Examples of Simplifying Expressions
Expressions that include a negative exponent can be simplified by first rewriting the expression with positive exponents.
Multiplying Two Factors with the Same Base
The rules for exponents begin with the rule for multiplying two factors with the same base.
Roots of Variables
Simplifying radicals with cube and other roots and variables.
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.