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Introduction to square root
A square root is a mathematical operation that extracts a number, called a root, from a number, called the radicand. The root is the number that, when multiplied by itself, equals the radicand. For example, the square root of 9 is 3, because 3 multiplied by 3 equals 9.
The symbol for square root is √.
What are Square Roots?
Square roots are a mathematical operation that takes a number and finds the square root of that number. For example, the square root of 64 is 8.
Finding Square Roots:
To find the square root of a number, you first have to identify the radical sign and determine which root is being sought. The radical sign identifies the root that is being squared. The square root of a number is the answer to the question “What number, when multiplied by itself, equals the given number?”
For example, the square root of 64 is 8 because 8 multiplied by 8 equals 64.
To find the square root of a number, divide the number by the number that is immediately below it on the number line. For example, the square root of 25 is 5 because 5 divided by 2 equals 25. If there is no number that is immediately below the number on the number line, then the square root cannot be found and the answer is undefined.
Finding Square Roots of Imperfect Squares
There is no one definitive way to find the square root of an imperfect square. One method is to use the quadratic equation to find the roots of the square, and then take the square root of the two roots. Another method is to use the Newton-Raphson algorithm to find the root of the square.
How to find the square root of imperfect numbers by long division method
When finding the square root of an imperfect number, divide the number by 2 until you reach a whole number. The square root of the number is the whole number that you divided by 2.
Properties of Square Root
The square root of a number is the number that, when multiplied by itself, results in the original number. For example, the square root of 9 is 3, because 3 multiplied by 3 results in 9.
The square root of a number can be found using a calculator, or it can be estimated using a method such as the trial and error method.
