# How do you write all the names that apply to -sqrt100?

Jun 11, 2017

Asking for "all" properties is impossible to fulfil - Anyway, some of the obvious ones are listed below.

#### Explanation:

Let $x = - \sqrt{100}$

(i) $x \in \mathbb{R}$

(ii) $x < 0$

(iii) $x = - \sqrt{{2}^{2} \times {5}^{2}} = - \left(2 \times 5\right) = - 10 \to x \in \mathbb{Z}$

(iv) ${x}^{2} = 100$

NB: There are an infinite number of possible properties that could be constructed to define $x$ in this example. Understanding that is probably more important than the ones listed above.