What is the easiest way to calculate square roots without me

[sofiajone]

Hi everyone,

I’ve been trying to understand square roots better, and I’m curious about the method people use when the number isn't a perfect square.

For example, with something like √27, I know that 25 is 5², so the answer has to be a little more than 5. But after finding the nearest perfect square, I’m not always sure how to get a more accurate decimal answer without simply guessing.

Do you normally estimate between two perfect squares, use the long-division method, or use an iterative method such as Newton’s method? I’m especially interested in a method that is easy to follow by hand but still gives a reasonably accurate answer.

For checking my final result after working it out manually, I sometimes use a square root calculator to compare the approximation with the calculated value.

What method do you find easiest for learning square roots, particularly for numbers that are not perfect squares?

[nycmath]

For the √27, break the square root into two parts. One part has to be a perfect square but the other does not.

We know that √27 = √9 • √3.

Notice that the √9 is a perfect square.
Also, √3 is already in lowest terms.

The √9 = 3.

Final answer is 3 √9