Square Root Formula
A number that on multiplication by itself gives the original number is called a square root. The inverse or reverse method of squaring a number is referred to as square root. Therefore, we can say that square and square roots are related concepts.
A number, which when squared gives the original number is generally said to be equal to the square root.
We can say if a is a positive integer, then
√ (a.a) = √(a2) = a
In mathematics, a one-to-one function that takes a positive number as an input and returns the square root of the given input number is given by a square root.
f(x) = √x
if x=16, then the function gives the solution as 4.
A negative number’s square root is always a complex number.
That means √-n = i√n, where i is said to be an imaginary number.
Symbol of Square Root
‘√’ this is the symbol used to denote the square root. It is also called a radical symbol.
For example, if ’x’ is a number then the square root can be written as
‘ √x ‘
Radicand is the number that appears to be under the radical symbol.
For example, a radical of 6 is used to represent the square root of 6. Both give the same value.
Let us take some examples of the Square Root Formula
1. Solve the radical equation √(4a+9) – 5 = 0
Given, √(4a+9) – 5 = 0
Let us first isolate the square root term.
Then the equation will become,
√(4a+9) = 5
Squaring on both the sides,
4a+9 = 52
4a + 9 = 25
4a = 16
a = 16/4
a = 4
2. What is the square root of 60?
Let us use the prime factorizing method to find the square root of 60
60 can be written as 2 × 2 × 3 × 5
= (2)2 × 3 × 5
By applying the square root formula, we get
√60 = [(2)2 × 15 ]1/2