What is the square root of 161?
Understand the Problem
The question asks for the square root of the number 161, which involves determining which number multiplied by itself equals 161. This is a straightforward mathematical calculation.
Answer
The square root of 161 is approximately $12.6886$.
Answer for screen readers
The square root of 161 is approximately $12.6886$.
Steps to Solve
- Identify the Problem
We need to find the square root of the number 161, which is denoted as $\sqrt{161}$.
- Estimate the Square Root
To estimate, we determine the squares of nearby integers. We know:
$$ 12^2 = 144 $$
and
$$ 13^2 = 169 $$
Since $144 < 161 < 169$, we can conclude that:
$$ 12 < \sqrt{161} < 13 $$
- Calculate an Approximation
Using a calculator or numerical method, we can find a more accurate value for $\sqrt{161}$. The calculation yields:
$$ \sqrt{161} \approx 12.6886 $$
- Final Result
Having estimated and calculated, the square root of 161 is approximately 12.6886.
The square root of 161 is approximately $12.6886$.
More Information
The square root represents a value which, when multiplied by itself, gives the original number. The number 161 is not a perfect square, which is why we get an approximation rather than an integer result.
Tips
- Miscalculating nearby squares. Always double-check the squares of numbers near your estimate.
- Assuming that square roots can only be whole numbers. Many numbers have irrational square roots.
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