Estimating Square Roots

 

Everybody knows that the square root of 4 is 2, but what about the square root of 85? How can one get a reasonable estimate of what the square root is? Give a quick estimate by following three simple steps:

Step 1: Find the nearest square root. In this case, the square root of 81 is 9

Step 2: Determine the next closes square root. In this case, the square root of 100 is 10

Step 3: Therefore, the square root of 85 is a value between 9 and 10. Since 85 is closer to 81, the actual value must be 9 point something

While this technique will not give you the exact answer, it certainly is useful if you want a quick estimate or to verify your answer.