Final answer:
To determine the value of n that makes the square root equation true, we simplified the square root of the fraction involving perfect square numbers and variables raised to an even power. However, additional information is required to find a specific value for n.
Step-by-step explanation:
The student is asking for the value of n that makes the square root equation √(225/625m⁴n⁶) true. To solve this, we need to simplify the square root. Since 225 and 625 are perfect squares, we can take the square root of 225 to get 15, and the square root of 625 to get 25. Furthermore, when taking the square root of variables raised to an even power, we divide the exponent by 2. Therefore, the exponent of m after taking the square root will be 2 (because 4 divided by 2 equals 2), and the exponent of n will be 3 (because 6 divided by 2 equals 3).
Thus, the simplified form of the square root equation becomes (15/25)m²n³.
To find the value of n that makes this equation true, we would need additional information on what the entire equation is supposed to equal or any additional constraints that are applied to n. Without this information, we can't provide a definitive value for n.
In general, n² represents a number raised to the second power, which is the number multiplied by itself. For example, for any integer value n, raising it to the fourth power would give us n times n raised to the third power, and so on for higher powers according to the equation n = n x n⁻¹.