To square root a fraction, you simply square root both the numerator and the denominator separately.
Understanding Square Roots of Fractions
Taking the square root of a fraction means finding a number that, when multiplied by itself, gives you the original fraction. Here's the general rule:
√(a/b) = √a / √b
Where:
- 'a' is the numerator (the top number)
- 'b' is the denominator (the bottom number)
Steps to Square Root a Fraction
- Identify the Numerator and Denominator: Clearly identify the top number (numerator) and the bottom number (denominator) of the fraction.
- Square Root the Numerator: Calculate the square root of the numerator.
- Square Root the Denominator: Calculate the square root of the denominator.
- Simplify (if possible): Reduce the resulting fraction to its simplest form, if necessary.
Example
Let's say you have the fraction 9/16. To find its square root:
- Numerator: 9
- Denominator: 16
- Square Root of the Numerator: √9 = 3
- Square Root of the Denominator: √16 = 4
Therefore, the square root of 9/16 is 3/4.
Practical Insights
- Perfect Squares: If both the numerator and denominator are perfect squares (like 9 and 16 in the example above), the square root will be a simple fraction.
- Non-Perfect Squares: If either the numerator or denominator (or both) are not perfect squares, you'll likely end up with a square root in the numerator and/or denominator. In these cases, the square root can be left in radical form or approximated with a decimal.
- Simplification is Key: Always reduce your resulting fraction to its simplest form. This will make things easier for future calculations.
Addressing the Reference
The reference ([Part of a video titled How do you take the Square Root of Fractions? Let's see… - YouTube]) seems to start with a different topic, "one over square root of 3" and then multiplying that by one, which is not directly addressing the core topic of how to square root a fraction in general. However, the core concept is the same: you must work with both numerator and denominator.
Table: Square Root Examples
| Fraction | Numerator Root | Denominator Root | Result |
|---|---|---|---|
| 4/25 | √4 = 2 | √25 = 5 | 2/5 |
| 16/49 | √16 = 4 | √49 = 7 | 4/7 |
| 1/100 | √1 = 1 | √100 = 10 | 1/10 |
| 5/9 | √5 | √9 = 3 | √5/3 |
| 2/3 | √2 | √3 | √2/√3 |
Important Note: In some cases such as √2/√3, you may have to rationalize the denominator by multiplying the numerator and denominator by √3, but that is beyond the scope of taking the square root of the fraction itself.
