Final answer:
The square root of a perfect square with an even number of zeros at the end will also have an even number of zeros, as the square root operation effectively halves the number of zeros.
Step-by-step explanation:
When a perfect square ends with an even number of zeros, the square root of such a square will have an even number of zeros. This relationship follows because if a number is a perfect square, it can be expressed as the product of an integer multiplied by itself. For instance, if a perfect square has four zeros, it can be thought of as squared of a number with two zeros. According to the rules of exponents (such as 5¹ × 5¹ = 5²), the square root effectively halves the exponent which is assigned to the trailing zero. Similarly, when dealing with perfect squares like (10²)² = 10´, taking the square root gives us 10², which has an even number of zeros. Therefore, for a perfect square with an even number of trailing zeros, its square root will also have an even number of trailing zeros.