Answer: (a) Jaclyn's reasoning is incorrect because she used the property that the square root of a product is equal to the product of the square roots. However, this property only holds true for non-negative numbers. In this case, Jaclyn used the square root of 25 to calculate the square root of 75, but 75 is not a perfect square, so its square root is not a rational number.
(b) To estimate the square root of 75, we can use a calculator or simplify the expression by factoring out perfect squares. We can factor 75 as 25 x 3, so
√75 = √(25 x 3) = √25 x √3 = 5√3 ≈ 8.7
Therefore, the square root of 75 to the nearest tenth is approximately 8.7.
Explanation: