Algebra 2: Solving Radical Equations

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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.

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:Screen Shot 2020-05-12 at 11.23.20 AM.pngStill not sure of their coolness? Let’s see what they look like with actual numbers:
Screen Shot 2020-05-12 at 11.24.21 AM.pngExample: Solve the following algebraic equation below for the missing variable (aka, solve for x).Screen Shot 2020-05-12 at 11.25.03 AM.pngExplanation:

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.Screen Shot 2020-05-12 at 11.26.21 AM.pngStep 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!Screen Shot 2020-05-12 at 11.29.11 AM.pngScreen Shot 2020-05-12 at 11.29.34 AM.pngWhat 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:Screen Shot 2020-05-12 at 11.30.21 AM.pngRemember, we know radicals can also be written as fractions: Screen Shot 2020-05-12 at 11.31.01 AM.pngTherefore 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:Screen Shot 2020-05-12 at 11.31.47 AM.pngWant more practice? Try solving these next few examples on your own. Screen Shot 2020-05-12 at 11.32.39 AM.pngWhen you’re ready, check out the below:Screen Shot 2020-05-12 at 11.33.12 AM.png

Did I miss anything?  Don’t let any questions go unchecked and let me know in the comments! Happy calculating! 🙂 

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