The square root of 40 can be expressed as a fraction by simplifying it. First, let’s find the square root of 40.
The square root of 40 is not a whole number, so we simplify it. We can break down 40 into its prime factors:
- 40 = 4 × 10
- 4 can be further broken down to 2 × 2, and 10 can be broken down to 2 × 5.
So, we can express 40 as:
- 40 = 2 × 2 × 2 × 5 = 23 × 5
Using the property of square roots, we can write:
√40 = √(4 × 10) = √4 × √10. Since we know that √4 = 2, we get:
√40 = 2 × √10.
To express this as a fraction, we typically write it with a denominator so that it fits the format of a fraction. Hence, we can represent the square root of 40 as:
√40 = 2√10 / 1
This is a valid representation; however, keep in mind that since √10 is an irrational number, this fraction does not represent a rational number but rather a simplified form of the square root of 40.
To make things clearer, if you need a decimal approximation, you can calculate:
√40 ≈ 6.324. So, while not a fraction in its traditional sense, if we need to represent it with numbers, we might say:
6.324 / 1.
In conclusion, while you can express the square root of 40 as a fraction in a way that maintains its form, the most precise simplified expression remains:
2√10.