The expression 65 √35x45. 8√28x is equivalent to axb, where a and b are positive constants and x > 1. What is the value of a + b?
Correct answer: A. 361/8
- A. 361/8
- B. 60
- C. 40
- D. 10
Explanation
The given expression is 65√35x45. 8√28x. To simplify, apply the properties of exponents and roots:Recognize that √35 is the same as (35)^(1/2) = 35/2.The expression becomes 65 * 35/2 * 45 * 28/2 * x1. Simplify further:Combine the exponents for common bases, and simplify the expression using properties of exponents: (6 * 4)5 * 35/2 * 24 * x.Calculate the coefficients: (24)5 = 65 * 45.Combine all terms to get a = 361/8 and b = 1. Thus, a + b = 361/8 + 1 = 369/8.Hence, the answer is 361/8. Other options result from incorrect simplification steps or arithmetic errors.
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Quantitative reasoning applies arithmetic and basic algebra to numerical relationships, including percentages, ratios, averages, fractions, proportions, profit and loss, rates, time, work and measurement. Questions focus on translating words into equations, choosing an efficient method and checking whether the result is numerically reasonable.
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