What is the square root of 999?
Understand the Problem
The question is asking for the square root of the number 999. This involves finding a number that, when multiplied by itself, equals 999.
Answer
$\sqrt{999} \approx 31.62$
Answer for screen readers
The approximate value of the square root of 999 is $\sqrt{999} \approx 31.62$.
Steps to Solve
- Initial Square Root Concept
To find the square root of 999, we need to determine which number, when multiplied by itself, gives 999. We can denote the square root symbol as $\sqrt{\cdot}$.
- Using a Calculator or Approximation
In practice, we can use a calculator to find an approximate value of $\sqrt{999}$. If we do not have a calculator, we can also approximate by noting that $31^2 = 961$ and $32^2 = 1024$. Since 999 lies between these two squares, we know that:
$$ 31 < \sqrt{999} < 32 $$
- Refining the Estimate
We can refine our estimate by considering a decimal value between 31 and 32. Testing for $31.5$:
$$(31.5)^2 = 992.25$$
This is still less than 999. Next, let's check $31.6$:
$$(31.6)^2 = 998.56$$
Still less than 999.
Next, we can check $31.7$:
$$(31.7)^2 = 1004.89$$
This is greater than 999.
- Conclusion on the Square Root
From our calculations, we find that:
$$ 31.6 < \sqrt{999} < 31.7 $$
Thus, we can conclude that the square root of 999 is approximately $31.62$ after rounding.
The approximate value of the square root of 999 is $\sqrt{999} \approx 31.62$.
More Information
The square root of a number is essentially one of the foundational concepts in mathematics, related to areas of geometry and algebra. Square roots can be both rational and irrational, with 999 being a non-perfect square.
Tips
- A common mistake is to misunderstand the range of the square root. Students may try to find the exact square root when it actually is an irrational number.
- Another mistake is only checking whole numbers without considering decimal values between them.
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