In general, we can approximate the value of a square root by observing the whole numbers around it and remembering the relationship between square roots and squares. Here are some examples:

• is a little more than 8 because is a little more than , and .
• is a little less than 9 because is a little less than , and .
• is between 8 and 9 (it’s 8 point something) because 75 is between 64 and 81.
• is approximately 8.67 because .

A number line with the numbers 8 through 9, in increments of zero point 1, are indicated. The square root of 64 is indicated at 8. The square root of 65 is indicated between 8 and 8 point 1, where the square root of 65 is closer to 8 point 1. The square root of 75 is indicated between 8 point 6 and 8 point 7, the square root of 75 is closer to 8 point 7. The square root of 80 is indicated between 8 point 9 and 9, where the square root of 80 is closer to 8 point 9. The square root of 81 is indicated at 9.

If we want to find the square root of a number between two whole numbers, we can work in the other direction. For example, since and , then we know that (to pick one possibility) is between 22 and 23. Many calculators have a square root command, which makes it simple to find an approximate value of a square root.