Question

For what values of the variable does each of the following expressions make sense? \sqrt((1 3a)/(25))

Answer 1

We can express this in interval notation as [-1/3, ∞). This interval indicates that a can take on any value from -1/3 up to positive infinity.

Step-by-step explanation:

To determine the values of the variable a for which the expression √{1 + 3a}/{25} makes sense, we need to consider the properties of square roots.

The expression inside a square root must be non-negative since the square root of a negative number is not defined in the set of real numbers.

Let's analyze the expression under the square root:
√{1 + 3a}/{25}

For this expression to be non-negative (meaning zero or positive), the numerator (1 + 3a) must be non-negative because the denominator is positive (25 is always positive).

Let's find when 1 + 3a ≥ 0:
1 + 3a ≥ 0
3a ≥ -1
a ≥ -1/3

Therefore, the values of a for which the original square root expression makes sense are all real numbers greater than or equal to -1/3.