Adding Square Roots – A Step-by-Step Guide

This article is a summary of the YouTube video ‘How to Add and Subtract Square Roots’ by TabletClass Math

Written by: Recapz Bot

Written by: Recapz Bot

AI Summaries of YouTube Videos to Save you Time

How does it work?
Simplify and combine like terms, add/subtract same square roots.

Key Insights

  • Key insights of the video on how to add and subtract square roots:
  • Adding and subtracting square roots involves simplifying and combining like terms.
  • The square roots being added or subtracted must be identical in order to perform the operation.
  • If the square roots are identical, you can add or subtract the numbers outside the square root symbol.
  • Fully simplify square roots by breaking them up into their factors.
  • Pay attention to positive and negative numbers when adding or subtracting square roots.
  • Practice and individual effort are essential to mastering these skills.
  • The video mentions additional resources, courses, and programs available for further learning in mathematics.

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Transcript

Okay, let’s talk about how to add and subtract square roots. So what am I talking about exactly? Well, I’m talking about dealing with problems like this. We have the square root of 8 and we would like to add it to the square root of 2. So what is the answer?

Now notice I said that we would like to add these up. Sometimes when you’re adding or subtracting square roots, we can’t really simplify the expression. You’ll see why here in a second. But what I’m not talking about is getting our calculator out and typing in the square root of 8 and getting some decimal and then typing in the square root of 2 and getting some decimal and adding them, adding those two up. That’s not what I’m talking about.

So let’s put our calculator, our calculators away except for the one between your ears. That one comes in pretty handy. So if you know what to do here, go ahead and type in your answer into the comment section because this is absolutely essential skills in any sort of algebra course.

Okay, so I’m going to get to exactly what we need to do to add and subtract square roots in just one second. But first, let me quickly introduce myself. My name is John. I’m the founder of Tablet Class Math. I’m also a middle and high school math teacher. I’m going to leave a link to my math help program in the description of this video. But I’ve been teaching math for decades and I really kind of developed a teaching style where I really explain things in a super clear and understandable way so anyone and everyone can learn mathematics and anyone and everyone can learn math. As long as you’re willing to do your part, I think I have the right instruction for you.

So if you’re at the middle school, high school, or college level and you need assistance in mathematics, definitely check out my math help program. Now if you happen to be preparing for some sort of test within math section, there’s a lot of those out there. I’m talking about things like the GED, SAT, ACT, CLEP exam, ACCUPLACER. If you’re going to college, you’ll be taking some sort of placement exam, a college entrance exam. But I’m also talking about tests like teacher certification exams and maybe nursing school entrance exams or the ASRAP for the military. All these different exams, I have test prep courses so I can help you prepare and pass those exams. If you homeschool, I was just recently voted in my middle and high school math courses number one for homeschooling by a major homeschool publication. Pretty excited about that. And if you need some math notes, I’m going to leave links to my math notes in the description of this video.

Okay, so let’s get into how to add and subtract square roots. So let’s take a look at some basic examples and we’ll get back to that example here in a second.

So let’s take a look at the square root of three plus four times the square root of three. So what is the answer? I’m going to go ahead and tell you the answer. The answer is five times the square root of three.

Okay, so how did I get that answer? So here you have the square root of three, but outside right here you really just have one square root of three or one times the square root of three. So this is just one square root of three. And then over here I have a square root of three, but I have four times the square root of three. So this is like having four square roots of three.

So if I have one square root of three over here and I have four square square roots of three over here. Okay, let’s kind of look at it this way, right? This is four times one square root of three. That means that you have four square roots of three. So here I have four square roots of three. I have one all together. Collectively we have five square roots of three.

Let’s take a look at this right here, this problem in another way. I want you to think of this square root of three and a square root of three like a variable. So here, let me just write it this way. We have one square root of three plus four square root of three. I want you to think of these here kind of like a variable. If you’re familiar with how to add like terms, let’s replace the square root of three with x. So I just have one x plus four x. So how many x’s total do we have? We have five x’s, okay?

So as long as you have the exact same square roots, okay? In other words, the square root of three and the square root of three, we simply just add these numbers here, okay? Now these numbers, the one and the four, these can be positive and negative numbers. So whatever these are, the sum of these numbers, you’re going to put that in front of the square root of three, okay?

So let’s take a look at some other problems here so we do not confuse this rule. So how about the square root of three plus four times the square root of two? How do we add these up? Well, I have a square root of three here and I have a square root of two here, okay? Are these exactly the same? Can I add these up? No, you cannot because this is a square root of three and this is a square root of two. We cannot add these up.

So to kind of use my algebra example, the

This article is a summary of the YouTube video ‘How to Add and Subtract Square Roots’ by TabletClass Math