Simplify square root of 0.563
Brief Explanation:
The question is asking you to perform a mathematical operation on a decimal number to find its square root. Simplifying the square root of a number involves finding a value that, when multiplied by itself, will yield the original number (in this case, 0.563). The task could involve either an exact calculation or an approximation, depending on whether the square root of 0.563 is a rational number (can be expressed as a fraction) or an irrational number (cannot be expressed as a fraction with finite length). The result should be a value that is easier to understand or work with than the original expression.
$\sqrt{0.563}$
Answer
Solution:
Step 1:
To simplify the square root of 0.563, we can express it in different ways. The exact form remains under the radical, while the decimal form is the approximation of the square root.
- Exact Form: $\sqrt{0.563}$
- Decimal Form: Approximately $0.75033325\ldots$
Knowledge Notes:
To understand the simplification of the square root of a decimal number, we need to be familiar with the following concepts:
Square Root: The square root of a number is a value that, when multiplied by itself, gives the original number. For example, the square root of 9 is 3, because $3 \times 3 = 9$.
Decimal Numbers: These are numbers that have a whole number part and a fractional part, separated by a decimal point.
Exact Form: When we talk about the exact form of a square root, we mean the square root symbol with the number inside it. This form does not provide a decimal approximation but represents the precise value.
Decimal Form: This is the approximate value of the square root to a certain number of decimal places. It is often obtained using a calculator or a numerical method like the Newton-Raphson method.
Approximation: Since the square root of most numbers cannot be expressed as a perfect whole number, we often use an approximate decimal value to represent the square root.
When simplifying the square root of a decimal like 0.563, we typically use a calculator to find the decimal approximation. The exact form is straightforward as it is simply the square root symbol with the number inside. The decimal form requires computation and is often rounded to a certain number of decimal places for practical use.
