What is a square root?

When a number is squared to \(n\), such a number is called the square root of \(n\).

As an example, consider the square root of 4.

The square root of 4 is ±2, since the numbers that square 4 are 2 and -2.

Similarly, considering the square root of 5, it is not easy to represent a number that squares to 5.

In this case, the square root of 5 is represented as \( \pm\sqrt{5} \).

Example

Example 1

Simplify \( \sqrt{169} \).

Solution

\[ \sqrt{169}=\sqrt{13^{2}}=13 \]

Example 2

Simplify \(\sqrt{2048}\).

Solution

\[ \sqrt{2048}=\sqrt{32^{2}\times2}=32\sqrt{2} \]