What is the value of a_Total = sqrt(5^2 + 7^2 + 10^2)?
Understand the Problem
The question is asking to calculate the value of a quantity called a_Total, which is the square root of the sum of the squares of 5, 7, and 10. This involves basic arithmetic operations: squaring, addition, and taking the square root.
Answer
$a_{Total} = \sqrt{174} \approx 13.2$
Answer for screen readers
$a_{Total} = \sqrt{174} \approx 13.2$
Steps to Solve
- Calculate $5^2$
$5^2 = 5 \times 5 = 25$
- Calculate $7^2$
$7^2 = 7 \times 7 = 49$
- Calculate $10^2$
$10^2 = 10 \times 10 = 100$
- Sum the squares
$25 + 49 + 100 = 174$
- Take the square root of the sum
$a_{Total} = \sqrt{174} \approx 13.2$
$a_{Total} = \sqrt{174} \approx 13.2$
More Information
The value $\sqrt{174}$ is an irrational number, meaning it cannot be expressed as a simple fraction. Thus, we often use approximations like 13.2.
Tips
A common mistake is to take the square root of each number individually before summing them. Remember to square each number, then add them together, and then take the square root of the result.
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