1. Find the exact solution to the equation 75=x2
, leaving your answer in square root form. Show your work.
2. State if your solutions are rational or irrational. Explain.
3. Find the closest integer approximation to your solutions and explain how you found them.
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.