In this video I will show you how to use Factor Trees to find the Square Root or simplify a square root! Factor trees are a great way to simplify square roots because you don’t have to use specific factors to get started – you can just start with what you know!
I will show you step by step, with plenty of examples, how to take any number and simplify it by breaking it down into it’s prime factors, and then what to do with those factors. I give examples of perfect square roots as well as numbers that don’t factor perfectly.
Transcript
0:00
This video is going to show you how to find the square root of numbers.
0:02
For example, if I’m trying to find the square root of 36, I know that 6 × 6 = 36. Therefore, the square root of 36 equals 6. It just means: what number can be multiplied by itself to get this number?
0:10
Here’s an example of a larger number. Let’s find the square root of a larger number like 225.
0:34
For larger numbers, I like to use prime factorization or a factor tree. If you don’t know what factor trees are, you can check out my other video on factor trees. I’ll put a link down in the comments below about factor trees—it could help you with this.
0:51
The first step when dealing with a larger number like this is to find the prime numbers that create this number.
1:00
I’m going to factor out 225. Because I know my divisibility rules, I know this number is divisible by 5 since there’s a 5 in the one’s place.
1:08
Let’s divide 225 by 5. Five goes into 22 four times (4 × 5 = 20), and then 5 goes into 25 five times. So, 225 = 5 × 45. This helps break it into smaller, more manageable chunks.
1:30
Five is a prime number, so I’ll circle it. I can still continue with 45. I know 45 = 5 × 9. Five is a prime number, so I’ll circle it as well.
1:49
Nine can be broken down into 3 × 3, and both of those are prime numbers.
2:03
I’ve now broken 225 into all its prime factors: 5, 5, 3, and 3. I’ll write these underneath the radical like so.
2:16
The rule with square roots is: if you have a partner, you can go outside the “house” (radical). That’s what I always tell my students.
2:21
Since 5 has a partner and 3 has a partner, they can go outside the house. These numbers outside the house are multiplied together. So, 5 × 3 = 15.
2:58
There’s nothing left inside the radical, so it goes away. The square root of 225 equals 15.
3:00
This one worked out nice and easy. It was perfectly even, with nothing left over.
3:11
What happens if you’re trying to find the square root of a number that doesn’t work out perfectly, like when it doesn’t result in a whole number?
3:18
Let’s try finding the square root of 360.
3:26
I’m going to use my factor tree again to factor 360. I know that 360 = 36 × 10.
3:33
I’ll break 36 into 6 × 6 and 10 into 2 × 5. Two and 5 are prime numbers, so I can stop there.
3:45
Next, I’ll break the sixes into 2 × 3 and 2 × 3. All of these (2, 3, 2, and 3) are prime numbers.
3:52
Now I’ve got all my prime factors for 360: 2 × 2 × 2 × 3 × 3 × 5.
4:07
The square root of 360 is the same as the square root of these factors.
4:12
You can’t go outside the house unless you have a partner. The 2s and the 3s each have a partner, but the 2 and 5 do not.
4:18
The numbers with partners (2 and 3) go outside the house. Inside the house, we’re left with 2 and 5.
4:32
Outside the house, multiply 2 × 3 = 6. Inside, multiply 2 × 5 = 10.
4:48
So, the square root of 360 simplifies to 6 times the square root of 10.
4:54
There you go! That’s how to find the square root using the factor tree and prime factorization.
5:00
I hope this video helps. Thanks so much! Bye.
Extra Credit
If you are looking for other math YouTube videos that pair well with this skill, try these:
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