Square root

What Is a Square Root?

A square root is a fun idea in mathematics. It helps us find a number that, when multiplied by itself, gives us another number. For example, the square root of 16 is 4, because 4 × 4 equals 16.

We write square roots using a special symbol called the radical sign or radix. It looks like this: √. So, we say √16 = 4. This tells us that 4 is the main, or principal, square root of 16.

A Long History

People have known about square roots for thousands of years! Ancient cultures like the Babylonians and Egyptians used them. One old Babylonian tablet from around 1800–1600 BC shows an early way to find the square root of 2.

Later, smart people in Ancient India made new ways to find square roots. The ancient Greeks found that some square roots, like the square root of 2, cannot be written as a simple fraction. These are called irrational numbers. The symbol we use today, √, first appeared in a book in 1525.

Why Square Roots Matter

Square roots are very useful. For example, if you know the area of a square, the square root can tell you the length of one side. Some square roots are easy, like √4 = 2. Others are long numbers that go on forever, like √2, which starts with 1.414…

Fun With Numbers

Here are a few simple square roots to try:

• √4 = 2 because 2 × 2 = 4
• √9 = 3 because 3 × 3 = 9
• √16 = 4 because 4 × 4 = 16

Square roots help us understand numbers better and are used in many parts of math and science.