What is the radical form of each of the given expressions?
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4 1/7
4 7/2
7 1/4
7 1/2
There are no radical expressions given, so there is no answer to this question.
To find the radical form of each given expression, we need to simplify the given mixed numbers.
1. The radical form of 4 1/7 is √(4 + 1/7).
2. The radical form of 4 7/2 is √(4 + 7/2).
3. The radical form of 7 1/4 is √(7 + 1/4).
4. The radical form of 7 1/2 is √(7 + 1/2).
Therefore, the correct matches are:
1. 4 1/7 -> √(4 + 1/7)
2. 4 7/2 -> √(4 + 7/2)
3. 7 1/4 -> √(7 + 1/4)
4. 7 1/2 -> √(7 + 1/2)
To find the radical form of each expression, we need to express each expression as a fraction and simplify the radical if possible.
Let's start with the first expression: 4 1/7
To express this mixed number as an improper fraction, we multiply the whole number (4) by the denominator of the fraction (7) and add the numerator (1). So, 4 1/7 is equal to (4 * 7 + 1)/7 = 29/7.
Now, let's simplify the radical. Since the expression is a fraction, we need to simplify the numerator and the denominator separately.
The square root of 29 is already in the simplest form, so it remains as √29.
The square root of 7 can be simplified as follows:
- We can break down 7 into its prime factors: 7 = 1 * 7.
- Since there are no repeated factors, we cannot simplify the √7 any further.
Therefore, the radical form of the expression 4 1/7 is √29/√7.
Repeat the same steps for the other expressions:
For 4 7/2:
- Convert 4 7/2 to an improper fraction: (4 * 2 + 7)/2 = 15/2.
- Simplify the square root of 15/2 by simplifying the numerator and denominator separately. The square root of 15 cannot be simplified any further, and the square root of 2 cannot be simplified either. So, the radical form of 4 7/2 is √15/√2.
For 7 1/4:
- Convert 7 1/4 to an improper fraction: (7 * 4 + 1)/4 = 29/4.
- Simplify the square root of 29/4 by simplifying the numerator and denominator separately. The square root of 29 cannot be simplified any further, and the square root of 4 is 2. So, the radical form of 7 1/4 is √29/2.
For 7 1/2:
- Convert 7 1/2 to an improper fraction: (7 * 2 + 1)/2 = 15/2.
- Simplify the square root of 15/2 by simplifying the numerator and denominator separately. The square root of 15 cannot be simplified any further, and the square root of 2 cannot be simplified either. So, the radical form of 7 1/2 is √15/√2.
To summarize:
4 1/7 = √29/√7
4 7/2 = √15/√2
7 1/4 = √29/2
7 1/2 = √15/√2