What is the square root of 280?
Understand the Problem
The question is asking for the square root of the number 280, which involves finding a number that, when multiplied by itself, equals 280.
Answer
$\sqrt{280} \approx 16.733$ or $2\sqrt{70}$
Answer for screen readers
The square root of 280 is approximately 16.733, or in simplest radical form, $2\sqrt{70}$.
Steps to Solve
- Estimate the square root range
The first step is to approximate the range within which the square root of 280 lies. We know that the square root of 256 is 16 ($ecause 16^2 = 256$) and the square root of 289 is 17 ($ecause 17^2 = 289$). Therefore, the square root of 280 must lie between 16 and 17.
- Refine the estimate
To get a more accurate value, we can refine our estimate further using a method such as the Newton-Raphson method or more precise calculation. However, a good approximation for practical purposes is around 16.73.
- Simplify the exact expression
To express the square root of 280 in simplest radical form, factorize 280 into its prime factors: $280 = 2^3 imes 5 imes 7$. Then, pair the factors to simplify: $\sqrt{280} = \sqrt{4 \times 70} = \sqrt{4} \times \sqrt{70} = 2\sqrt{70}$.
- Final numerical approximation
For the final numerical approximation, you can use a calculator to get a more precise decimal value. $\sqrt{280} \approx 16.733$.
The square root of 280 is approximately 16.733, or in simplest radical form, $2\sqrt{70}$.
More Information
The square root function is fundamental in various fields of science and engineering, often used in calculations involving areas and quadratic equations.
Tips
A common mistake is in not simplifying the radical expression correctly. Ensure you factorize completely and pair the factors properly.
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