Simplify 13 square root of 3

Solution:

Step 1:

The expression can be represented in different ways. Here are two common representations:

• Exact Form: $13\sqrt{3}$
• Decimal Form: $13\times 1.73205080757\approx 22.51666049$

Knowledge Notes:

To simplify the expression $13\sqrt{3}$, we need to understand that there are generally two ways to represent square roots: in their exact form or as decimal approximations.

1. Exact Form: This is the form in which the square root is left as is, without converting it to a decimal. It is an exact representation of the value and is commonly used in mathematical and scientific calculations to avoid rounding errors. In this case, the exact form is $13\sqrt{3}$.

2. Decimal Form: This is the approximate form of the square root, where the square root value is converted into a decimal. To convert $\sqrt{3}$ into a decimal, we can use a calculator or recognize that $\sqrt{3}$ is approximately $1.73205080757$. Multiplying this by 13 gives us the decimal approximation of the original expression: $13\times 1.73205080757\approx 22.51666049$. This form is useful for practical measurements or when a numerical approximation is sufficient.

In mathematics, the square root of a number $x$ is a value that, when multiplied by itself, gives the number $x$. The square root of 3 is an irrational number, meaning it cannot be expressed as a simple fraction and its decimal representation goes on infinitely without repeating. The symbol for the square root is $\sqrt{}$. When dealing with square roots, it is important to consider the context to decide whether an exact or decimal form is more appropriate.