# Write The Expression 6 7/12 In Radical Form

## 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:

1. 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.
2. 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.

Android62 is an online media platform that provides the latest news and information about technology and applications.