How to Estimate Square Roots

What Is a Square Root and a Radicand?

A square root is a number that when multiplied by itself, results in its original number. For example, the square root of 16 is 4 because 4 • 4 = 16.

A radicand is the value that you want to find the root of. For example, 16 is the radicand of 4 because 16 is the value that you want to find the root of, which is 4.

Estimating Square Roots

In our example, we will be estimating the square root of 28. Remember, the answer will not be exact, but it should be near the exact answer. To find the estimated square root, we will be using a number line. Find the two numbers closest to the square root that you are using. In this example, since we are using v28, the two closest radicands are v25 and v36. Draw a number line like the one that you see below. v28 is much closer to v25 than v36, so we can cross out the numbers 5.5 and higher. 5.1 and 5.2 seem too close to the square root of 25, and 5.4 seems just a little too big for the square root of 25. That only leaves us with 5.3, which is correct. The estimated square root of v28 is 5.3. You can also double check it by using a calculator and finding the exact square root of 28, 5.2915026..., which, when rounded to the nearest tenth is 5.3.