What is the square root of 404?
Understand the Problem
The question is asking for the square root of the number 404. To solve it, we will find a number that, when multiplied by itself, equals 404.
Answer
The square root of 404 is approximately $20.10$.
Answer for screen readers
The square root of 404 is approximately $20.10$.
Steps to Solve
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Identifying the Operation We need to find the square root of 404, which we represent as $\sqrt{404}$.
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Approximating the Square Root First, we can estimate the square root by finding two perfect squares that surround 404. The nearest perfect squares are $20^2 = 400$ and $21^2 = 441$. This tells us that: $$ 20 < \sqrt{404} < 21 $$
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Using a Calculator for Precision Using a calculator, we find the square root of 404 more precisely. This gives us: $$ \sqrt{404} \approx 20.09975124224178 $$
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Rounding to Desired Precision If we need to round to a reasonable decimal place, we can round to two decimal places: $$ \sqrt{404} \approx 20.10 $$
The square root of 404 is approximately $20.10$.
More Information
The square root of a number represents a value that, when multiplied by itself, gives that number. Square roots can often be estimated through the knowledge of nearby perfect squares, and calculators provide greater precision.
Tips
- Overlooking Perfect Squares: Some may forget to identify the perfect squares surrounding the number, which can help with estimation.
- Rounding Errors: Rounding too early in the calculations might lead to inaccurate results. Always calculate accurately first, then round.
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