The value of $(\sqrt{3})^2$ is $3$.

When you square a square root, you effectively reverse the square root operation. The square root of a number is defined as a value that, when multiplied by itself, yields the original number. For instance, the square root of $3$ (denoted as $\sqrt{3}$) is a number that, when squared (or multiplied by itself), returns the original number $3$.

This relationship can be mathematically expressed as:

This occurs because the square root and the square are inverse operations. The value of the square root of $3$ is approximately $1.732$, and when you square $1.732$, you arrive back at $3$. This principle holds true for any number: squaring the square root of a number will always return that original number.

Grasping this concept is essential in GCSE Maths, as it aids in simplifying expressions and solving equations that involve square roots. For example, if you come across an equation such as $x = \sqrt{3}$ and need to determine $x^2$, you can directly conclude that $x^2 = 3$ without any additional calculations. This understanding can save time and minimize errors in more complex problems.