Monkey Raptor

Tuesday, May 13, 2014

Math: (Shortcut for) Simplifying (Denesting) Nested Square Roots

This is a senior high Algebra material.
If you're teaching (or tutoring) or probably still in high school, this method is kinda easy to understand. Kinda.

The basic form looks like this :

two nested radical

Let's go to the methods and examples


The plus thingy

simplifying two nested radical with plus sign
√4 + √3 = 2 + √3

The minus thingy

simplifying two nested radical with plus sign
I forgot to put how to come up with 12 = 4 · 3 and 56 = 8 · 7.
The simplest way is to factor the number within the last square root. Then find the ones which if added will produce the first number.

For instance √(8 + 2√15)

We have 8 as the first number and 15 as the last one.
Factors of 15 :
  • 1 · 15 = 15
  • 3 · 5 = 15
Therefore, we choose the 2nd one, the 3 · 5 = 15
because 3 + 5 = 8
So we have x = 3 and y = 5
We put all together : √(8 + 2√15) = √3 + √5

Trick #1

trick #1 of simplifying two nested radical

Trick #2

trick #2 of simplifying two nested radical

If you wanna clarify the simplified forms above, you can go to Wolfram Alpha ➡ then type the complicated-er forms from my examples.

This is fun.

Math: (Shortcut for) Simplifying (Denesting) Nested Square Roots
https://monkeyraptor.johanpaul.net/2014/05/math-shortcut-for-simplifying-denesting.html

4 comments

  1. What if the nested radicand doesnt have any coefficient.

    ReplyDelete
    Replies
    1. What about that? Please be more specific by writing an example problem of that, or you could link an image/url.

      Delete

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