## 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) = √(a^{2}) = 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

For example,

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**

**Solution:**

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,

we get

4a+9 = 5^{2}

4a + 9 = 25

4a = 16

a = 16/4

a = 4

**2. What is the square root of 60?**

**Solution:**

Let us use the prime factorizing method to find the square root of 60

we get,

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}

√60

= 2√15