Final answer:
The square root of 9 over 25 is calculated by taking the square root of the numerator (9, which is 3) and the denominator (25, which is 5), resulting in the fraction 3/5. This utilizes the concept of fractional powers and properties of exponents.
Step-by-step explanation:
The student is asking how to represent 9 over 25 inside a square root. We can simplify this by first understanding the square root of a fraction. The square root of a fraction is the square root of the numerator divided by the square root of the denominator. In this case, we take the square root of 9 (which is 3) and the square root of 25 (which is 5).
So, the square root of 9/25 can be simplified as:
- √(9/25) = √9 / √25 = 3/5
- This result shows that the square root of the fraction 9/25 simplifies to the fraction 3/5.
This is based on the concept of fractional powers and the properties of exponents, which indicate that x² = √x. Using the same principle, we can solve the square root of a fraction like 9/25 by applying the square root to both the numerator and the denominator separately.