Final answer:
To find the square of 49.5, we square both 4.95 and 10, since 49.5 is ten times 4.95. Thus, (49.5)^2 equals (4.95)^2 multiplied by 10^2, resulting in 2450.25.
Step-by-step explanation:
To solve the question "If (4.95)^2 = 24.5, what is the value of (49.5)^2?" We need to understand the property of exponents when it comes to scaling up. The given number 49.5 is exactly ten times larger than 4.95. When we square 49.5, it is equivalent to squaring 4.95 and then squaring 10, according to the properties of exponents. Hence, (49.5)^2 = (4.95 × 10)^2 = (4.95)^2 × (10)^2.
Given (4.95)^2 = 24.5, we can then find (49.5)^2 by multiplying 24.5 by 10^2 which is 100. So, (49.5)^2 = 24.5 × 100 = 2450. Therefore, the correct answer is b. 2450.25.