If you are given the radical expression,√𝑥 − 4, what is the restriction on the value of x? Explain
The given radical expression is √x - 4.
In this case, the value inside the square root, x, must be greater than or equal to 4 for the expression to be defined and avoid taking the square root of a negative number.
If x is less than 4, the expression will result in the square root of a negative number, which is not a real number.
Therefore, the restriction on the value of x is x ≥ 4.
The radical expression √𝑥 − 4 represents the square root of 𝑥 minus 4. In order for this expression to be defined, the value inside the square root (√𝑥 − 4) must be non-negative.
To find the restriction on the value of 𝑥, we set the expression inside the square root to be greater than or equal to zero:
√𝑥 − 4 ≥ 0
Solving this inequality:
√𝑥 ≥ 4
Since the square root of 𝑥 must be greater than or equal to 4, 𝑥 itself must be greater than or equal to 16. This means that the restriction on the value of 𝑥 is 𝑥 ≥ 16. Any value of 𝑥 that is 16 or greater will make the radical expression √𝑥 − 4 defined.
To determine the restriction on the value of 𝑥 in the radical expression √𝑥 − 4, we need to consider the domain of the square root function.
The square root function (√𝑥) is defined only for non-negative values of 𝑥. When 𝑥 is negative, the square root of 𝑥 is not a real number. In this particular expression, √𝑥 − 4, the square root term (√𝑥) is subtracted by 4.
In order to avoid taking the square root of a negative number, the expression inside the square root (√𝑥) must be greater than or equal to 0. Setting √𝑥 - 4 ≥ 0, we can solve it for 𝑥:
√𝑥 - 4 ≥ 0
Adding 4 to both sides:
√𝑥 ≥ 4
To eliminate the square root, we square both sides:
(√𝑥)² ≥ 4²
𝑥 ≥ 16
Therefore, the restriction on the value of 𝑥 in the radical expression √𝑥 − 4 is 𝑥 ≥ 16. This means 𝑥 must be greater than or equal to 16 in order for the expression to be defined.