simplifying basic radical expressions
DESCRIPTION
TRANSCRIPT
![Page 1: Simplifying basic radical expressions](https://reader035.vdocuments.us/reader035/viewer/2022081413/54840d8db4af9f7d0d8b4a78/html5/thumbnails/1.jpg)
S
Simplifying Basic Radical Expressions
By L.D.
![Page 2: Simplifying basic radical expressions](https://reader035.vdocuments.us/reader035/viewer/2022081413/54840d8db4af9f7d0d8b4a78/html5/thumbnails/2.jpg)
Table of Contents Slide 3: What is a Radical? Slide 4: Instructions For The Problems Slide 5: Problem 1 Slide 11: Problem 1 Example Problems Slide 13: Problem 2 Slide 16: Problem 3 Slide 18: Problem 4 Slide 21: Problem 5
![Page 3: Simplifying basic radical expressions](https://reader035.vdocuments.us/reader035/viewer/2022081413/54840d8db4af9f7d0d8b4a78/html5/thumbnails/3.jpg)
What is a Radical?
“Radical” is a fancy name for a square root. A radical expression is an expression with a square root.
![Page 4: Simplifying basic radical expressions](https://reader035.vdocuments.us/reader035/viewer/2022081413/54840d8db4af9f7d0d8b4a78/html5/thumbnails/4.jpg)
Instructions For The Problems
Simplify the problems until there are no perfect squares under the square roots.
![Page 5: Simplifying basic radical expressions](https://reader035.vdocuments.us/reader035/viewer/2022081413/54840d8db4af9f7d0d8b4a78/html5/thumbnails/5.jpg)
Problem 1
√24
![Page 6: Simplifying basic radical expressions](https://reader035.vdocuments.us/reader035/viewer/2022081413/54840d8db4af9f7d0d8b4a78/html5/thumbnails/6.jpg)
Problem 1
√24Your first thought when seeing this problem is probably that 24 is not a perfect square. This can easily be fixed.
![Page 7: Simplifying basic radical expressions](https://reader035.vdocuments.us/reader035/viewer/2022081413/54840d8db4af9f7d0d8b4a78/html5/thumbnails/7.jpg)
Problem 1
√24The first step to solve this problem is to find the factors to 24. I personally like the cake method (if you do not know how to use this method, check the post on my blog titled “GCF & LCM” since it has a how-to). Factors: 3, 2, 2, 2
![Page 8: Simplifying basic radical expressions](https://reader035.vdocuments.us/reader035/viewer/2022081413/54840d8db4af9f7d0d8b4a78/html5/thumbnails/8.jpg)
Problem 1
√24Factors: 3, 2, 2, 2Now we have the factors we need to choose two of them that are the same number, we have two 2s. They can be multiplied to make 4 and the leftover numbers 3 & 2 can be multiplied for 6. We will put these numbers with a multiplication sign under a square root sign
![Page 9: Simplifying basic radical expressions](https://reader035.vdocuments.us/reader035/viewer/2022081413/54840d8db4af9f7d0d8b4a78/html5/thumbnails/9.jpg)
Problem 1
√6 x 4 can also be seen as √6 x √4 . We will simplify the square root we can now simplify(√4 ). The problem will now look like 4 x √6 or 4√6 .
![Page 10: Simplifying basic radical expressions](https://reader035.vdocuments.us/reader035/viewer/2022081413/54840d8db4af9f7d0d8b4a78/html5/thumbnails/10.jpg)
Problem 1
Our final answer is 4√6 as there are no more factors that are hidden in the numbers under the square roots.
![Page 11: Simplifying basic radical expressions](https://reader035.vdocuments.us/reader035/viewer/2022081413/54840d8db4af9f7d0d8b4a78/html5/thumbnails/11.jpg)
Problem 1 Example Problems
1. √50
2. √48
![Page 12: Simplifying basic radical expressions](https://reader035.vdocuments.us/reader035/viewer/2022081413/54840d8db4af9f7d0d8b4a78/html5/thumbnails/12.jpg)
Problem 1 Example Problems
1. √50 = √25 x 2 = 5√2
2. √48In this problem we will get the factors 2, 2, 2, 2 & 3. Since we have two sets of two we will make the 2s combine to be what is below. √48 = √16 x 3 = 4√3
![Page 13: Simplifying basic radical expressions](https://reader035.vdocuments.us/reader035/viewer/2022081413/54840d8db4af9f7d0d8b4a78/html5/thumbnails/13.jpg)
Problem 2
√25g5
![Page 14: Simplifying basic radical expressions](https://reader035.vdocuments.us/reader035/viewer/2022081413/54840d8db4af9f7d0d8b4a78/html5/thumbnails/14.jpg)
Problem 2
√25g5
To find the answer to this we will as usual find the factors.Factors: 5, 5, g, g, g, g & gWe will do as usual and multiply all the doubles together.
![Page 15: Simplifying basic radical expressions](https://reader035.vdocuments.us/reader035/viewer/2022081413/54840d8db4af9f7d0d8b4a78/html5/thumbnails/15.jpg)
Problem 2
√25g5
Factors: 5, 5, g, g, g, g & g√25g5 = √25g4 x g = 5g2√g
![Page 16: Simplifying basic radical expressions](https://reader035.vdocuments.us/reader035/viewer/2022081413/54840d8db4af9f7d0d8b4a78/html5/thumbnails/16.jpg)
Problem 3
√7 x √7
![Page 17: Simplifying basic radical expressions](https://reader035.vdocuments.us/reader035/viewer/2022081413/54840d8db4af9f7d0d8b4a78/html5/thumbnails/17.jpg)
Problem 3
√7 x √7Remember how we can split numbers under separate square roots, well we can also put them back together. √7 x √7 = √7 x 7 = √49 = 7
![Page 18: Simplifying basic radical expressions](https://reader035.vdocuments.us/reader035/viewer/2022081413/54840d8db4af9f7d0d8b4a78/html5/thumbnails/18.jpg)
Problem 4
3√k x √2k3
![Page 19: Simplifying basic radical expressions](https://reader035.vdocuments.us/reader035/viewer/2022081413/54840d8db4af9f7d0d8b4a78/html5/thumbnails/19.jpg)
Problem 43√k x √2k3
First we will combine the things under the square roots.3√k x √2k3 = 3√2k4
Now we will find the factors of the thing under the square root.Factors: 2, k, k, k & k
![Page 20: Simplifying basic radical expressions](https://reader035.vdocuments.us/reader035/viewer/2022081413/54840d8db4af9f7d0d8b4a78/html5/thumbnails/20.jpg)
Problem 4Factors: 2, k, k, k & kWe have two sets of k so our problem will be shown below.3√2 x k4 = 3 x k2 √2 = 3k2√2
![Page 21: Simplifying basic radical expressions](https://reader035.vdocuments.us/reader035/viewer/2022081413/54840d8db4af9f7d0d8b4a78/html5/thumbnails/21.jpg)
Problem 5
√5/49
![Page 22: Simplifying basic radical expressions](https://reader035.vdocuments.us/reader035/viewer/2022081413/54840d8db4af9f7d0d8b4a78/html5/thumbnails/22.jpg)
Problem 5
√5/49To solve this problem we must first split it, we will put square root signs over both and then solve.√5/√49 = √5/7
![Page 23: Simplifying basic radical expressions](https://reader035.vdocuments.us/reader035/viewer/2022081413/54840d8db4af9f7d0d8b4a78/html5/thumbnails/23.jpg)
Visit
myratatemyhomework.blogsp
ot.com for m
ore math
tutorials!