Praxis Core Academic Skills for Educators: Mathematics (5733)Number and QuantityEasy
A civil engineer is calculating the strength of a beam. The formula involves (5^2 + 12^2)^1/2. What is the result of this calculation?
- A17
- B169
- C289
- D13
Show answer & explanationAnswer & explanation
Correct answer: D. 13
First, calculate the squares: 5^2 = 25 and 12^2 = 144. Then, add them: 25 + 144 = 169. Finally, take the square root (exponent of 1/2): (169)^1/2 = 13. This is a Pythagorean triple (5, 12, 13).
Why the other options are wrong
- A. This might result from adding the bases (5+12) and then squaring or taking the square root, which is incorrect.
- B. This is the sum of the squares (169) but without taking the square root.
- C. This is the square of the sum of the bases (5+12)^2 = 17^2, which is incorrect.
Order of Operations (PEMDAS/BODMAS)
A set of rules that dictate the sequence in which mathematical operations should be performed to ensure a consistent result.
- Parentheses/Brackets first.
- Exponents/Orders next.
- Multiplication and Division (from left to right).
- Addition and Subtraction (from left to right).
Memory trick: Power up, then dig deep for the root!