Mathematics » Roots and Radicals » Simplify Square Roots

Defining Simplify Square Roots

In the last topic, we estimated the square root of a number between two consecutive whole numbers. We can say that \(\sqrt{50}\) is between 7 and 8. This is fairly easy to do when the numbers are small enough that we can use (see this lesson).

But what if we want to estimate \(\sqrt{500}\)? If we simplify the square root first, we’ll be able to estimate it easily. There are other reasons, too, to simplify square roots as you’ll see later in this tutorial.

A square root is considered simplified if its radicand contains no perfect square factors.

Simplified Square Root

\(\sqrt{a}\) is considered simplified if \(a\) has no perfect square factors.

So \(\sqrt{31}\) is simplified. But \(\sqrt{32}\) is not simplified, because 16 is a perfect square factor of 32.

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