1. To find the exact solution to the equation 75 = x^2, we need to take the square root of both sides of the equation:
√75 = √(x^2)
Since the square root of a product is equal to the product of the square roots, we can simplify this as:
√(25 * 3) = x
Taking the square root of 25 gives us:
√25 = x
Therefore, the exact solution to the equation is x = ±√25.
2. The solutions for x = ±√25 are rational numbers. This is because the square root of 25 is a whole number (5), and rational numbers can be expressed as fractions or decimals.
3. The closest integer approximations to the solutions x = ±√25 are x ≈ ±5. This is because the square root of 25 is exactly 5, and the closest integers to 5 are 5 and -5.