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Since we don’t have to write 2 as an index, the answer is √j. Example 1: Write √15 as an expression with fractional exponents. Solution: The index of √15 is 2, and we have 1 as the power of the radicand. Therefore, our fractional exponent is ½. Thus, √15 = 15 1/2. Example 4: Write a 3/4 as a radical expression.
Using Fractional Exponents to Describe Roots. The laws of exponents suggest an exponential notation for roots involving fractional exponents. For instance, applying the exponent rules to the expression a1/2, we get. Thus, a1/2 should be the number whose square is a, so we define. Similarly, we define.
General Solution Steps: Step 1. Isolate the Radical(s) and identify the index (n). Step 2. Raise both sides of the equation to the “nth” power. Step 3. Use algebraic techniques (i.e. factoring, combining like terms,...) to isolate the variable. Repeat Steps 1 and 2 if necessary. Step 4. Check answers.
The parts of this expression are: ) “a” – The ‘index’, or the “root” of the expression. ) “ a ” – The ‘radical’ symbol. ) “ x n ” – The radicand. This expression can be rewritten as a fractional power on ‘ x ’ of the form: x n / a , where a , n∈Z.
Radical Equations. A radical equation is any equation that contains one or more radicals with a variable in the radicand. Following are some examples of radical equations, all of which will be solved in this section: √x − 1 = 5 √2x − 5 + 4 = x 3√x2 + 4 − 2 = 0.
1 Radical Equations. An equation that has the variable to be solved for inside a radical is called a radical equation. The algebraic manipulations (described below) needed to solve the equation for the variable can be involved, and may result in extraneous solutions.
