# Square Root Formula

When a value is multiplied by itself to give the original number then that number is a square root. Represented by a radical symbol $\sqrt{}$ “Square Root” is often used to refer to the principal square root.

For example, 4 and -4 are the square roots of 16 because 42 is 16.

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

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 perfect square, its square root is 6.

### SOLVED EXAMPLES

**Question 1:** What is the square root of 144?

**Solution:**

The factors of 144 are given as,

144 = 12××12

$\sqrt{144}=12\times 12$

**Question 2:** What is the square root of 80?

**Solution:**

The factors of 80 are given as,

$80 = \sqrt{4\times 4\times 5}$

$80=\sqrt[4]{5}$

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