Square root of 313
Understand the Problem
The question is asking for the mathematical calculation of the square root of the number 313. This requires step by step computation to find the principal square root value.
Answer
\approx 17.692
Answer for screen readers
The approximate value of the square root of 313 is 17.692.
Steps to Solve
- Identify the range of the square root value
Notice that the number 313 is between 289 (which is $17^2$) and 324 (which is $18^2$), so the square root of 313 must be between 17 and 18.
- Use a calculator for more precise value
For a more precise result, you can use a calculator or an estimate method to find the square root value: $$ \sqrt{313} \approx 17.692 $$ 3. Verify through squaring
Verify the estimated solution by squaring it:
$$ 17.692^2 \approx 313 $$, which confirms that the value is correct.
The approximate value of the square root of 313 is 17.692.
More Information
The square root is a value that, when multiplied by itself, gives the original number. The square root of 313 is an irrational number, meaning it cannot be expressed as a simple fraction.
Tips
A common mistake is to estimate outside the correct range, so always check the nearest perfect squares first to narrow down the range.
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