What is one way to estimate a square root?

Estimating a square root can effectively be achieved by identifying the nearest perfect square. Perfect squares are whole numbers obtained by squaring integers, such as 1, 4, 9, 16, 25, etc. By finding the perfect squares that closest surround the number in question, one can determine a reasonable estimate for its square root.

For example, if you want to estimate the square root of 10, you recognize that 9 (3²) and 16 (4²) are the nearest perfect squares. Since 10 is closer to 9 than to 16, you can deduce that the square root of 10 is slightly above 3. This method provides a quick and intuitive way to approximate square roots without needing a calculator.

The other options, while they may involve mathematical operations, do not consistently yield accurate approximations for square roots. For instance, using the average of two numbers does not directly relate to finding a square root, dividing the number by two does not typically lead to a useful estimate, and finding prime factors is a method more suited for simplifying expressions rather than estimating square roots. Therefore, identifying the nearest perfect square stands out as the most effective and reliable technique for estimation in this context.