Solving Radical Equations: Algebra 2/Trig.

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Today we’re back with Algebra 2, this time solving for radical equations!  Did you say “Radical Equations?” As in wild and crazy equations? No, not exactly, radicals in math are used to take the square root, cubed root, or whatever root of a number.

Solving Radical Equations
Solving Radical Equations

Example #1:

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Radicals are actually pretty cool because we can write them a couple of different ways and they all mean the same thing! Check it out below:Still not sure of their coolness? Let’s see what they look like with actual numbers:
Example: Solve the following algebraic equation below for the missing variable (aka, solve for x).Explanation:

How do I answer this question?   

The question wants us to solve for x using our knowledge of radicals and algebra. You can also check out how to solve this question on Youtube here!

How do we do this? 

Step 1: We start solving this radical equation like any other algebraic problem: by getting x alone. We can do this easily by subtracting 7 and then dividing out 5.

Solving Radical Equations

Step 2: Now, to get rid of that pesky radical, we need to square the entire radical.  Remember, whatever we do to one side of the equation, we must also do to the other side of the equation, therefore, we also square 14 on the other side of the equal sign. *This gets rid of our radical and allows us to solve for x algebraically as normal!

Solving Radical Equations
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What happens when there is a cubed root though!?!?

When dividing polynomials with different value roots, raise the entire radical to that same power of root to cancel it out:Remember, we know radicals can also be written as fractions:

Solving Radical Equations

Therefore we also know that if we raise the entire radical expression to the same power of the root, the two exponents will cancel each other out:

Solving Radical Equations

Example #2:

Solving Radical Equations

Want more practice? Try solving radical equations in the next few examples on your own. 

Practice:

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Solutions:

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Looking to brush up on how to solve absolute value equations? Check out the post here! Did I miss anything?  Don’t let any questions go unchecked and let me know in the comments! Happy calculating! 🙂 

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