Continuing the discussion from Hectoc Strategies:

Say you got a HECTOC starting with:

```
552___ for 5x5x2 = 50
522___ for 52-2 = 50
455___ for 45+5 = 50
```

…or another sequence of 3 digits that easily gets you to **50**. Next you’d want to get a **2** on the right hand side for a nice **50x2 = 100**; however, the **next digit is a 4** and **you don’t have a square root** available (only +, -, x, ÷, ^, and parenthesis)… or do you?

```
___412 for 4^(1/2) = 2
___424 for 4^(2/4) = 2
___436 for 4^(3/6) = 2
___448 for 4^(4/8) = 2
```

You can simply use the exponential form of the square root by using the reciprocal of 2 as your exponent. Similarly you can **use a cube root by using 1/3** (i.e., the reciprocal of 3):

```
___813 for 8^(1/3) = 2
___826 for 8^(2/6) = 2
___839 for 8^(3/9) = 2
```

For those not familiar with the exponential form, this will continue 1/4, 1/5, etc.

`826416 for (8+2)^(64^(1/6)) = 10^2`

2^6 = 64 so thesixth rootof 64 is 2 again

Alternatively, you could of course use 82+6x4x1-6 like any normal person would; but it’s certainly nice to have the additional option of square roots, cube roots, etc. available even though “officially” you don’t… they’re just hidden in plain sight.