Final answer:
The square root of the fraction with numerator 1 + 3a and denominator 25 is the square root of 1 + 3a divided by the square root of 25, which simplifies to the square root of 1 + 3a over 5.
Step-by-step explanation:
To find the square root of the fraction with numerator 1 + 3a and denominator 25, you should take the square root of both the numerator and the denominator separately. The square root of 25 is 5. So, we can express the square root of the entire fraction as:
√1 + 3a}/25 = √1 + 3a/√25 = 1 + 3a/5
This expresses the original fraction under a square root as a fraction with a radical only in the numerator. Thus, the answer is (1 + 3a) / 5.
This process follows a general principle of simplifying fractions with radicals. The goal is to express the fraction in a form that is easier to work with and understand.
Such simplifications are common in algebraic manipulations, making expressions more manageable in various mathematical contexts.