E. Estimating Radicals

Estimating the value of an irrational radical can be useful for determining its approximate magnitude. This can be helpful when evaluating the reasonableness of solutions to real-life problems, such as measurements.

Estimations can be done by hand on paper or mentally, without a calculator, with a certain level of accuracy.

For example, using ; consider the first number smaller than 20 that is a perfect square (that has a Whole Number square root) and the first number larger than 20 that is a perfect square (that has a Whole Number square root).

Example 1

4
4.4 or 4.5
5

The value 20 is about half way between 16 and 25, so the square root of 20 will be about half way between 4 and 5, or approximately 4.4 or 4.5.

Using a calculator, the decimal equivalent of is 4.472135955....

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