What is the square root of 202?
Understand the Problem
The question is asking for the square root of the number 202, which is a mathematical operation that finds a value that, when multiplied by itself, gives the number 202.
Answer
The square root of 202 is approximately $14.21$.
Answer for screen readers
The square root of 202 is approximately $14.21$.
Steps to Solve
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Identify the operation To find the square root, we need to express this mathematically. The square root of a number $x$ is denoted as $\sqrt{x}$. In this case, we need to find $\sqrt{202}$.
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Approximate using prime factorization To approximate $\sqrt{202}$, we can factor 202. The prime factorization of 202 is $2 \times 101$, where both 2 and 101 are prime numbers.
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Determine the range of the square root Since $14^2 = 196$ and $15^2 = 225$, we know that $\sqrt{202}$ lies between 14 and 15.
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Refine the approximation Using a numerical method or calculator, we can find a more precise value.
Calculating gives:
$$ \sqrt{202} \approx 14.21 $$
- Present the final value Now we can summarize our final answer for the square root of 202.
The square root of 202 is approximately $14.21$.
More Information
The square root of 202 is an irrational number, meaning it cannot be expressed as a simple fraction. The approximation of $14.21$ is useful for various practical applications.
Tips
- Not recognizing that the square root is between two whole numbers, which can lead to miscalculating the range.
- Forgetting that the square root of a non-perfect square is an irrational number.
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