The square root formula helps in representing any number in the form of its square root. The square root of any number is that value, which when multiplied with itself gives the original number. It is represented using "√" symbol. Every number has two square roots, one with a positive value, and the other negative. Let us understand the square root formula using solved examples in the following section.
What Is the Square Root Formula?
The square root of any number is given as the number raised to the power 1/2. While calculating the square root of any number, we take both the negative and positive values as the square root after calculation. The square root formula for a perfect square would give an integer as the result. The square root of a negative number can never be a real number.
Square Root Formula
The square root formula of a number, x is given as,
√x = x1/2
Suppose, x is any number such that, x = y × y, the formula to calculate the square root of x will be,
√x = √(y × y) = y
where, y is the square root of any number x. This also means that if the value of y is an integer, then x would be a perfect square.
Methods for Square Root Formulas
Although there are different methods that can be conveniently used for perfect squares, the long division method can be used for any number whether it a perfect square or not.
In math, the square root formula is used to represent any number in the form of its square root, such as for any number x, its square root will be √x = x1/2
What Is the Square Root Formula for Negative Numbers?
We know that the negative numbers don't have real square roots. The square roots of numbers other than a perfect square are considered irrational numbers. The principal square root of any negative numbers, say -x is: √(-x)= i√x, where, i is the square root of -1.
What Are the Applications of the Square Root Formula?
There are a varied number of applications of the square root formula
It has uses in algebra and geometry. It acts as a base for the formula of roots of a quadratic equation; quadratic fields and rings of quadratic integers.
It is frequently used in many physical laws.
To calculate areas, volumes, and other measurement formulas.
Widely used by carpenters, architects, and engineers.
How To Write Square Root Formula in Words?
The square root of any number is the number raised to the power of 1/2.