Last Updated on September 30, 2020 by A Plus In-Home Tutors
As an Algebra Tutor in the Laguna Hills area, I’ve noticed Algebra students struggling greatly with radicals and finding square roots. It’s one thing to simplify the square root of an integer, but it’s an entirely other thing to simplify the square root of a term that combines an integer with variables.
Let’s start at the beginning and lay the groundwork for “radical basics” when it comes to these types of Algebra problems.
Radical Algebra With Perfect Squares
Let’s begin with a simple radical expression: √81
In this problem, we have a radical (that “square root thing”), and we have the number inside the radical called the radicand. As an Algebra Tutor, one way I like to think of the radicand is that it’s a number that has been put in “radical prison.” That 81 is trapped inside the radical, and the only way out of prison is to find a perfect square.
In Algebra, to break the 81 out of radical prison, we must consider whether it is, indeed, a perfect square. The term “perfect square” simply means that a number multiplied by itself equals the number in question. In this case, 81 is the perfect square of 9, since 9×9 is equal to 81.
Since 81 is indeed a perfect square, we can “break it out of radical prison” by removing the radical and simply writing: 9.
But before you box your answer right now, hold on for one second.
Radical Algebra Key to Remember
Whenever you break something out of radical prison, always always always remember to include both the positive and negative versions of that perfect square. While positive 9 times positive 9 indeed equals positive 81, negative 9 times negative 9 also equals positive 81. You could write your complete answer like this, using the symbol which stands for “plus or minus 9”: ±9
Algebra students often forget to include the negative perfect square in these types of problems. Don’t forget this important key!
Radical Algebra Without Perfect Squares
Many Algebra students require the help of an Algebra Tutor involving non-perfect squares with radicals. Take the following example: √32
Since 32 is not a perfect square, we cannot break it out of radical prison as easily as the previous problem. However, we can simply break it down into a partial perfect square by considering its factors.
Since the numbers 4, 9, 16, 25, 36, 49, etc. are all perfect squares, try dividing one of these critical numbers into the radicand in question.
In this case, the perfect square 16 divides into the imperfect square 32. Thus, we could rewrite our radicand as such: √(16×2)
Since we know the perfect square of 16 is 4, we can break a “plus or minus 4” out of radical prison, leaving our poor imperfect 2 behind in radical prison: ±4√2
Whenever you find yourself struggling to solve numerical radicand problems in Algebra, always remember the “plus or minus,” and always break down imperfect squares into at least one other perfect factor.
Remember these radical tips, and you’re well on your way to Algebra success.
And next time, I’ll cover the basics for solving radical Algebra problems with variables!
For a “radical” Algebra tutor in Laguna Hills or your surrounding area, please visit https://www.aplusinhometutors.com.