Explanation: To convert the fraction 129/225775 ​into decimal form, you simply divide the numerator by the denominator: 129/225775 ≈ 0.00057197 So, the decimal form of 129/225775 is approximately 0.00057197.

Explanation: To find the highest common factor (HCF) of 8, 9, and 25, you can use various methods like prime factorization, division method, or listing factors. Let's use the division method: 1. Find the factors of each number: Factors of 8: 1, 2, 4, 8 Factors of 9: 1, 3, 9 Factors of 25: 1, 5, 25 2. Identify the common factors among the numbers: Common factors: 1 3. The greatest common factor (HCF) is 1. So, the HCF of 8, 9, and 25 is 1.

Explanation: To determine which of the given expressions is not irrational, let's analyze each one: a. (2−3)2(2 - \sqrt{3})^2(2−3)2: • (2−3)2=4−43+3=7−43(2 - \sqrt{3})^2 = 4 - 4\sqrt{3} + 3 = 7 - 4\sqrt{3}(2−3)2=4−43+3=7−43 • This expression involves subtraction and multiplication by a rational number, so it could potentially be rational or irrational. b. (2+3)2(\sqrt{2} + \sqrt{3})^2(2+3)2: • (2+3)2=2+26+3=5+26(\sqrt{2} + \sqrt{3})^2 = 2 + 2\sqrt{6} + 3 = 5 + 2\sqrt{6}(2+3)2=2+26+3=5+26 • This expression involves addition and multiplication by a rational number, so it could potentially be rational or irrational. c. (2−3)(2+3)(\sqrt{2} - \sqrt{3})(\sqrt{2} + \sqrt{3})(2−3)(2+3): • (2−3)(2+3)=2−3=−1(\sqrt{2} - \sqrt{3})(\sqrt{2} + \sqrt{3}) = 2 - 3 = -1(2−3)(2+3)=2−3=−1 • This expression results in a rational number, since it involves subtraction of irrational numbers. d. 27727\sqrt{7}277: • This expression involves multiplication by an irrational number, so it's irrational. Therefore, the expression in option (c) (2−3)(2+3)(\sqrt{2} - \sqrt{3})(\sqrt{2} + \sqrt{3})(2−3) (2+3) is not irrational. It evaluates to a rational number, -1.

Explanation: The sum of a rational and an irrational number can be either rational or irrational, depending on the specific numbers being added. For example: • The sum of 12\frac{1}{2}21 (rational) and 2\sqrt{2}2 (irrational) is irrational (12+2\frac{1}{2} + \sqrt{2}21+2). • The sum of 12\frac{1}{2}21 (rational) and −2-\sqrt{2}−2 (irrational) is also irrational (12−2\frac{1}{2} - \sqrt{2}21−2). • However, the sum of 12\frac{1}{2}21 (rational) and 12\frac{1}{2}21 (rational) is rational (12+12=1\frac{1}{2} + \frac{1}{2} = 121+21=1). So, the correct answer is: (b) irrational