# What is #sqrt(12+sqrt(12+sqrt(12+sqrt(12+sqrt(12....)))))#?

##### 2 Answers

#### Explanation:

There is a really interesting math trick behind it.

If you see a question like this take out the number inside it (in this case is

Take consecutive numbers such as:

Always remember that the answer is

This is true because if you let the infinite nested radical function = x then realise that x is also also under the first root sign as:

Then, squaring both sides:

Or:

Now let

Then

If you solve it you get

So,

The answer is

**Practice problems:**

And wait!!!

If you see a question like

**Problems to solve on your own**

Better luck!

There is an other method to solve this

#### Explanation:

First of all, consider the whole equation equals

#color(brown)(sqrt(12+sqrt(12+sqrt(12....)))=x#

We can also write it as

#color(brown)(sqrt(12+x)=x#

As, the

Square both sides

When we simplify this, we get

From this, we get,