Pearson Algebra 2 Common Core, 2011
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Pearson Algebra 2 Common Core, 2011 View details
5. Solving Square Root and Other Radical Equations
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Exercise 30 Page 395

Raise each side of the equation to the reciprocal of the rational exponent. Remember to check your solutions.

Practice makes perfect
To solve equations with a variable expression raised to a rational exponent, we first want to make sure the variable expression is isolated. Then we raise each side of the equation to the reciprocal of the rational exponent.
Remember, if is even, then In this case so we do not need to worry about this.

Finding the Solutions

We will first isolate the variable expression raised to a rational exponent, and then raise each side of the equation to the power of
We now have a quadratic equation, and we need to find its roots. To do it, let's identify the values of and
We can see that and Let's substitute these values into the Quadratic Formula.
Solve for and Simplify
Using the Quadratic Formula, we found that the solutions of the given equation are Therefore, the solutions are and Let's check them to see if we have any extraneous solutions.

Checking the Solutions

We will check and one at a time. Let's start by substituting into the original equation.
Simplify left-hand side
We got a true statement, so is a solution. Let's now substitute
Simplify left-hand side
In this case we also got a true statement. Therefore, and are the solutions of the original equation.