Simplify 13 square root of 3
The question asks you to perform a mathematical simplification of the expression provided: "13 square root of 3." This typically involves simplifying or rewriting the given algebraic expression to a more basic or more easily understandable form without changing its value. In this case, you would need to apply the rules of arithmetic and algebra to the square root and the accompanying coefficient, if possible, to simplify the expression. However, since "13 square root of 3" is already in its simplest radical form (assuming there are no further instructions or context given), there would typically be no further simplification required.
$13 \sqrt{3}$
Answer
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.
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 $13\sqrt{3}$.
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.
