# What is the domain of sqrt 20 - x?

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The domain for the square root of (20-x) is x must be <= 20 real numbers. If x > 20, then the radicand becomes negative, which is fine, but not for real numbers. If x < 0, then 20 - (-x) becomes positive for all real number values for x.

Therefore, the domain can be stated as -∞ ≤ x ≤ 20.

You must follow the rule concerning the square roots: what is found under the radical sign is called radicand and it must be positive or zero.

The radicand is 20 - x.

`20 - xgt= 0`

Subtract 20 both sides:

`-x gt= - 20`

Multiply by -1:

`x =lt 20 ` (notice that the inequality has changed)

**ANSWER: The domain of `sqrt (20-x)` is the interval `(-oo;20].` **