Question

What is the restriction on the variable x for the radical
`\sqrt{48x^(2)}`?

A) x has to be greater or equal to 0
B) x can be any real number
C) x must be an even integer
D) x must be a prime number

Answer 1

The restriction on the variable x for the radical √48x² is that x can be any real number; there are no restrictions on x since the square of a real number is always non-negative.

Step-by-step explanation:

The student is asking about the restriction on the variable x within the radical √48x². A square root is defined as a number which, when multiplied by itself, will result in the number under the radical. Since 48x² is under a square root, we are considering the principal square root, which is always non-negative. This means that the value inside the square root, 48x², must also be non-negative, because the square of any real number is non-negative. Given that x², the square of x, will always be non-negative regardless of the value of x (since a negative number times a negative number is positive), the expression inside the square root will always be non-negative regardless of x. Therefore, x can be any real number and there are no restrictions on the values x can take with respect to non-negativity.