Square Root Formula

When a value is multiplied by itself to give the original number then that number is a square root. It is represented by a radical symbol
\(\begin{array}{l}\sqrt{}\end{array} \)
. “Square Root” is often used to refer to the principal square root. Here. we will discuss how to find the square root of a number using the square root formula, and important maths tricks for the square roots in detail.

Square root

For example, 4 and -4 are the square roots of 16. The formula to represent the square root is given below:

\[\LARGE \sqrt[n]{x}=x^{\frac{1}{n}}\]

Maths Tricks for Square Roots

There are different methods and tricks to find the square root of a number. They are:

  • Using Long Division Method
  • The square root of perfect squares using the prime factorisation method
  • Approximation of square root of a number for not a perfect square numbers.

Also, read:

Here, the easiest method trick to find the square root of a number is given below:

In order to calculate the square root, we first need to find the factors of a given number, then group the common factor together. Group the pairs separately if the factors have any perfect square. The square root of the square of a number is the number itself.

For example, the number 36 The factors of 36 is given as 6 x 6. Since it is a perfect square, its square root is 6.

Solved Examples

Question 1:

What is the square root of 144?


The factors of 144 are given as,
144 = 12×12

\(\begin{array}{l}\sqrt{144}=\sqrt{12\times 12}\end{array} \)
\(\begin{array}{l}\sqrt{144}=12\end{array} \)

Question 2:

What is the square root of 80?


The factors of 80 are given as,

80= 4×4×5

\(\begin{array}{l}\sqrt{80} = \sqrt{4\times 4\times 5}\end{array} \)
\(\begin{array}{l}\sqrt{80} = 4\sqrt{5}\end{array} \)


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