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 58 Page 396

Raise each side of the equation to the power of the denominator of the rational exponent.

Practice makes perfect
To solve equations with a variable expression raised to a rational exponent, we can raise each side of the equation to the power of the denominator of the rational exponent.
Since this will eliminate the root. In our case, we will first isolate the variable term and raise each side of the equation to the power of

We now have a polynomial, and we need to find its roots. The Rational Root Theorem can help us narrow down the possible roots. Let be a polynomial with integer coefficients. There are a limited number of possible roots for

Integer Roots

Integer roots must be factors of The constant term for our polynomial is Its factors, and the possible integer roots, are and Let's check them.

We can see above that is a root for the polynomial. Let's now try to find rational roots.

Other Possible Roots

Since is a solution for the polynomial, is factor of the polynomial. Let's use synthetic division to factor out Then we can find other roots using the remaining polynomial.

Bring down the first coefficient

Multiply the by the

Add down

Repeat the process for all the coefficients

Multiply the by the

Add down

Multiply the by the

Add down

Using synthetic division to remove the first root left us with the following polynomial.

Factoring the Remaining Quadratic Factor

We will use the Quadratic Formula to find the remaining factors. To do so, we will need to identify the values of and
We can see above that and Now, let's substitute these values into the Quadratic Formula to find the remaining roots.
Solve for and Simplify
The other two roots for the polynomial are and which are complex numbers. Therefore, the only real root for the polynomial is