# Radical Algebra in Laguna Hills

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.*