Understanding Mixed Numbers and Radicals
Before we delve into converting the expression 6 7/12 into radical form, let’s first review the concepts of mixed numbers and radicals.
- Mixed Numbers: A mixed number is a combination of a whole number and a fraction. For example, 3 1/2 is a mixed number where 3 is the whole number and 1/2 is the fraction part.
- Radicand: In mathematics, the expression underneath a radical symbol is called the radicand. For example, in the square root of 16, 16 is the radicand.
Converting a Mixed Number to Radical Form
Converting a mixed number to radical form involves expressing the given number as a single fraction and simplifying if necessary.
Step-by-Step Guide:
- Convert the Mixed Number to Improper Fraction: In our case, we have 6 7/12. To convert it to an improper fraction, multiply the whole number (6) by the denominator of the fraction (12) and add the numerator (7). This gives us (6 * 12) + 7 = 79. So, 6 7/12 is equivalent to 79/12.
- Express the Improper Fraction as a Radical: To express 79/12 in radical form, we need to find a way to write the fraction under a radical sign. To do this, we can express it as the square root of (79/12).
Calculating the Radical Form of 6 7/12
Now that we have converted 6 7/12 into the improper fraction 79/12, let’s calculate its radical form by expressing it as the square root of (79/12).
Calculating the Square Root:
To simplify the square root of 79/12, we need to find the factors of the numerator and denominator.
- Factorization of 79: The factors of 79 are 1 and 79 as it is a prime number.
- Factorization of 12: The factors of 12 are 1, 2, 3, 4, 6, and 12.
Since 79 is a prime number and cannot be simplified further, we leave it inside the radical. For the denominator 12, we can simplify it by recognizing that 12 is the product of 4 and 3.
Therefore, the expression 6 7/12 in radical form is √79/12.
Using Decimal Form as well
Converting the Fraction to Decimal:
In some cases, expressing a fraction as a decimal can provide a clearer representation of the number.
To convert 79/12 to a decimal, we divide 79 by 12. The result is approximately 6.5833.
Radical Form and Decimal Form:
So, the expression 6 7/12 can be represented in radical form as √79/12 and in decimal form as approximately 6.5833.
Conclusion
In conclusion, understanding how to convert a mixed number like 6 7/12 into radical form involves converting it to an improper fraction and expressing it under the radical sign. By following the step-by-step guide and simplifying the expression, we were able to find the radical form of 6 7/12 as √79/12. Additionally, we also converted the fraction to a decimal for a different representation. Mastering these conversions can be useful in various mathematical calculations and applications.
