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How to Estimate Square Roots (Radicals)

 
In mathematics, it is sometimes important for us to be able to estimate the values of square roots (radicals). This is especially the case on exams that do not allow the use of a calculator, and you try to eliminate wrong answers, or verify the reasonableness of your response. Also in the geometry, the values sqrt(2) and SQRT(3) come up so often that it is important to know their approximate values.

This article shows you the steps to estimate a square root. The article assumes that you have a basic understanding of square roots and perfect squares. See the Reference for more information.

1. In order to assess the value of the square root of a number, find the perfect squares are above and below the number. For example, to estimate the sqrt (6), note that 6 is between the perfect squares 4 and 9. SQRT (4) = 2, and sqrt (9) = 3. Since 6 is closer to 4 than it is to 9, we'd expect its square root to be closer to 2 than it is to 3. It is actually about 2.4, but as long as you knew, it was in this ballpark, you'd be fine. Even just to know that it was somewhere between 2 and 3 would be to your advantage.

2. Let's try another example. Assessment sqrt (53). 53 is between the perfect squares 49 and 64, the square roots, which are 7 and 8, respectively. 53 is closer to 49 than at 64, so it would be reasonable to estimate the sqrt (53) to be between 7 and 7.5. It turns out that it is around 7.3.

3. There are two square roots that come up very often in geometry. They are sqrt(2) and SQRT(3). It is very important that you remember their approximate values. Note that sqrt (1) is 1, and sqrt (4) is 2. . Based on this, it should come as no surprise that sqrt(2) is approximately 1.4, and SQRT(3) is approximately 1.7. The most important thing is to remember that sqrt(2) is greater than 1, and sqrt (3) is less than 2. another article discusses the application of these square roots in working with right triangles and the Pythagorean theorem.

4. Students should ensure that they are comfortable with estimating square roots, and for that matter estimating all your answers to see if they are reasonable. This will usually allow you to catch your mistakes before you hand in your exams.
 
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