To divide square roots, you can simply divide the numbers (radicands) inside the square root symbol and then place the result under a single square root. Here's a breakdown:
Dividing Square Roots: The General Rule
The core principle for dividing square roots is:
√(a) / √(b) = √(a/b) where b ≠ 0
In simpler terms, the quotient of square roots is equal to the square root of the quotient of the radicands.
Steps for Dividing Square Roots
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Identify the Radicands: Determine the values inside each square root symbol. These are called radicands.
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Divide the Radicands: Divide the radicand of the numerator (top) by the radicand of the denominator (bottom).
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Place Under a Radical: Put the result of the division under a single square root symbol.
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Simplify (If Possible): Simplify the resulting square root, if possible. This might involve finding perfect square factors within the radicand.
Examples
Here are some examples to illustrate the process:
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Example 1: √(16) / √(4)
- Divide the radicands: 16 / 4 = 4
- Place under a radical: √(4)
- Simplify: √(4) = 2
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Example 2: √(50) / √(2)
- Divide the radicands: 50 / 2 = 25
- Place under a radical: √(25)
- Simplify: √(25) = 5
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Example 3: √(12) / √(3)
- Divide the radicands: 12 / 3 = 4
- Place under a radical: √(4)
- Simplify: √(4) = 2
Table Summary
| Step | Description | Example |
|---|---|---|
| 1. Identify Radicands | Determine the numbers inside the square root symbols. | √(16) / √(4) -> 16 and 4 |
| 2. Divide Radicands | Divide the numerator's radicand by the denominator's radicand. | 16 / 4 = 4 |
| 3. Place Under Radical | Put the result of the division under a square root symbol. | √(4) |
| 4. Simplify (If Possible) | Simplify the resulting square root, if the radicand has perfect square factors. | √(4) = 2 |
Important Note
This rule applies only when you are dividing square roots. It does not apply to other operations like addition or subtraction. Also, ensure that you simplify the final square root to its simplest form whenever possible.
