Final answer:
The square root of 1+3a/25 is defined for real number values of a that are ≥ -25/3, to ensure the radicand is non-negative.
Step-by-step explanation:
The expression square root of 1+3a/25 makes sense for values of the variable a that ensure the expression under the square root, known as the radicand, is non-negative. This is because the square root of a negative number is undefined in the set of real numbers.
To find the values for which the expression is defined, we set the radicand to be greater than or equal to zero:
1 + (3a/25) ≥ 0
Multiplying both sides by 25 to clear the fraction gives:
25 + 3a ≥ 0
Subtracting 25 from both sides, we get:
3a ≥ -25
Dividing by 3, we find the range of a:
a ≥ -25/3
So, the expression makes sense for any real number a that is greater than or equal to -25/3.