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

The basic form looks like this:

Let's go to the methods and examples.

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PLUS

√4 + √3 = 2 + √3

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MINUS

This is how we 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 2^nd 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

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Trick #1

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Trick #2