List prime numbers between 100 and 120 and find the product of the largest and smallest. Classify 1, 2, and sqrt(5) as rational or irrational. Calculate the fraction of journey covered.

Here is the solution to your math problems: 6. Prime numbers and their product Step 1: List prime numbers between 100 and 120. A prime number is a natural number greater than 1 that has no positive divisors other than 1 and itself. The prime numbers between 100 and 120 are: 101, 103, 107, 109, 113 Step 2: Identify the largest and smallest prime numbers. Smallest prime number = 101 Largest prime number = 113 Step 3: Calculate the product of the largest and smallest prime numbers. Product = 101 × 113 101 × 113 = 11413 The product of the largest and smallest prime numbers is 11413. 7. Classification of numbers Step 1: Define rational and irrational numbers. A rational number can be expressed as a fraction (p)/(q) where p and q are integers and q ≠ 0. An irrational number cannot be expressed as a simple fraction; its decimal representation is non-terminating and non-repeating. Step 2: Classify the given numbers. 1: This can be written as (1)/(1). Therefore, 1 is a rational number*. 2: This can be written as (2)/(1). Therefore, 2 is a rational number*. sqrt(5): The square root of 5 is approximately 2.2360679..., which is a non-terminating and non-repeating decimal. Therefore, sqrt(5) is an irrational number*. 8. Fraction of journey covered Step 1: Determine the total time for the journey. Total time = 5 hours. Step 2: Determine the fraction of the journey covered in 1 hour. Fraction covered in 1 hour = 1 hour5 hours = (1)/(5). Step 3: Use reciprocal tables to find the value of (1)/(5). From reciprocal tables, the reciprocal of 5 is 0.2. (1)/(5) = 0.2 The fraction of the journey covered in 1 hour is 0.2. 9. Evaluation using mathematical tables Step 1: Evaluate (1)/(0.981) using reciprocal tables. From reciprocal tables, (1)/(0.981) ≈ 1.01936799... Rounding to 5 decimal places for intermediate calculation: 1.01937 Step 2: Evaluate (1)/(9.81) using reciprocal tables. From reciprocal tables, (1)/(9.81) ≈ 0.101936799... Rounding to 5 decimal places for intermediate calculation: 0.10194 Step 3: Add the results. 1.01937 + 0.10194 = 1.12131 The value is approximately 1.1213. 10. Laws of indices Step 1: Rewrite the expression using fractional exponents. 3/(81) = ((256)/(81))^(1)/(3) Step 2: Express the numbers as powers of their prime factors. 256 = 2^8 81 = 3^4 Step 3: Substitute these into the expression. ((2^8)/(3^4))^(1)/(3) = ((2^8)^1)/(3)(3^4)^(1)/(3) = (2^8)/(3)3^(4)/(3) Step 4: Simplify the exponents. 2^(8)/(3) = 2^2 + (2)/(3) = 2^2 · 2^(2)/(3) = 4 · [3]2^2 = 4 [3]4 3^(4)/(3) = 3^1 + (1)/(3) = 3^1 · 3^(1)/(3) = 3 [3]3 Step 5: Combine the terms. 4 [3]43 [3]3 To rationalize the denominator, multiply the numerator and denominator by [3]3^2 = [3]9. 4 [3]43 [3]3 × [3]9[3]9 = 4 [3]4 × 93 [3]3 × 9 = 4 [3]363 [3]27 = 4 [3]363 × 3 = 4 [3]369 The simplified expression is 4 [3]369. 11. Evaluation using logarithm tables Let x = (0.724 × 20.37)/(608). Step 1: Take the logarithm base 10 of both sides. _10 x = _10 ((0.724 × 20.37)/(608)) Step 2: Apply logarithm rules. _10 x = _10 (0.724) + _10 (20.37) - _10 (608) Step 3: Find the logarithms of each number using tables. _10 (0.724): Characteristic is 1. Mantissa of 724 is 0.8597. So, _10 (0.724) = 1.8597. _10 (20.37): Characteristic is 1. Mantissa of 2037 is 0.3090. So, _10 (20.37) = 1.3090. _10 (608): Characteristic is 2. Mantissa of 608 is 0.7839. So, _10 (608) = 2.7839. Step 4: Perform the addition and subtraction. _10 x = 1.8597 + 1.3090 - 2.7839 _10 x = ( -1 + 0.8597 ) + ( 1 + 0.3090 ) - ( 2 + 0.7839 ) _10 x = -1 + 0.8597 + 1 + 0.3090 - 2 - 0.7839 _10 x = (-1 + 1 - 2) + (0.8597 + 0.3090 - 0.7839) _10 x = -2 + (1.1687 - 0.7839) _10 x = -2 + 0.3848 _10 x = 2.3848 Step 5: Find the antilogarithm of 2.3848. The mantissa is $0.3848