What is the square root of 420?
Understand the Problem
The question is asking for the square root of the number 420, which involves finding a value that, when multiplied by itself, equals 420.
Answer
$20.49$
Answer for screen readers
The square root of 420 is approximately $20.49$.
Steps to Solve
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Identify the number to find the square root of
We are looking for the square root of 420. This means we need to find a value ( x ) such that ( x^2 = 420 ). -
Use a calculator or a method to approximate the square root
To calculate the square root of 420, we can either use a scientific calculator or apply an approximation method. We find: $$ \sqrt{420} \approx 20.49 $$ -
Verify the calculation
To confirm our result, we can square the answer: $$ 20.49^2 \approx 420 $$
The square root of 420 is approximately $20.49$.
More Information
The square root of 420 is not a whole number, but it is around 20.49. The precise square root can be expressed in radical form as $ \sqrt{420} = \sqrt{4 \cdot 105} = 2\sqrt{105} $.
Tips
- Rounding errors: When approximating the square root, ensure you carry enough decimal places to avoid significant rounding errors.
- Forgetting to square the result to check: Always verify that the square of your answer returns to the original number.
