Understanding the Square Root | Definition, Examples, and Applications

square root

The square root of a number is a mathematical operation that gives you the value which, when multiplied by itself, equals the original number

The square root of a number is a mathematical operation that gives you the value which, when multiplied by itself, equals the original number. In simpler terms, it is the number that, when squared, gives the original number as a result.

For example, the square root of 9 is 3, because 3 multiplied by itself equals 9 (3 x 3 = 9). Similarly, the square root of 16 is 4 (4 x 4 = 16).

The symbol used to represent the square root is √ (called the radical sign). For instance, √9 represents the square root of 9.

It’s important to note that there can be two square roots for any positive number, one positive and one negative. For example, both +3 and -3 are square roots of 9, because (3 x 3 = 9) and (-3 x -3 = 9).

When dealing with square roots of negative numbers, we enter the realm of complex numbers. The square root of -9, for example, is written as √-9, and the result is 3i, where i represents the imaginary unit (√-1).

Square roots are often used in various mathematical concepts, such as solving quadratic equations, calculating the side lengths of squares, and finding the distance between two points in coordinate geometry.

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