Dividing a radical expression by a whole number involves treating the whole number as a coefficient and simplifying the radical if possible. Here's a breakdown of the process:
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Write the expression as a fraction. Place the radical expression over the whole number. For example, if you want to divide √5 by 2, write it as √5 / 2.
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Simplify the radical (if possible). Look for perfect square factors within the radical. If you find any, simplify them. For example, √8 can be simplified to 2√2.
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Divide the coefficient of the radical by the whole number (if possible). If the whole number divides evenly into the coefficient of the radical, perform the division. For instance, if you have 6√3 / 2, you can divide 6 by 2 to get 3√3.
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If the whole number does not divide evenly into the coefficient of the radical, leave the expression as a fraction. This is your simplified answer. For example, √5 / 2 is already in its simplest form because √5 cannot be simplified further, and 1 (the implicit coefficient of the radical) cannot be divided evenly by 2.
Examples:
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Example 1: Divide √5 by 2. The answer is √5 / 2.
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Example 2: Divide √8 by 2.
- First, simplify √8 to 2√2.
- Now you have 2√2 / 2.
- Divide the coefficient 2 by the whole number 2, resulting in 1√2, which is simply √2.
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Example 3: Divide 6√3 by 2.
- Divide the coefficient 6 by the whole number 2, resulting in 3√3.
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Example 4: Divide (4 + √5) by 2.
- You can write this as (4 + √5)/2.
- Divide each term in the numerator by the denominator: 4/2 + √5/2
- Simplify: 2 + √5/2
In summary, dividing a radical by a whole number involves writing the expression as a fraction, simplifying the radical if possible, and then dividing the coefficient of the radical by the whole number if it's divisible. Otherwise, the expression remains a fraction.
