Question

For what values of the variable does each of the following expressions make sense? 3\sqrt(a)

Answer 1

The values of the variable a for which the expression
`\(3√(a)\)` makes sense are
`\(a \geq 0\)`.

The expression
`\(3√(a)\)` makes sense for values of a that ensure the square root operation is defined. In this case, the expression requires a non-negative value for the square root.

For the expression
`\(3√(a)\)` to make sense:

1. a must be greater than or equal to 0 because the square root of a negative number is undefined in the real number system.

2. a can be any real number, including 0, and the expression will be meaningful.

Therefore, the values of the variable a for which the expression
`\(3√(a)\)` makes sense are
`\(a \geq 0\)`.