The square root of 40 can be expressed as a fraction, but first, we should simplify it.
The square root of 40 can be broken down into its prime factors:
- 40 = 4 × 10
- 4 = 2 × 2
- 10 = 2 × 5
So, we have:
√40 = √(4 × 10) = √4 × √10
Now, √4 equals 2. Therefore:
√40 = 2 × √10
Although √10 cannot be simplified into a fraction, we can represent it in decimal form. The approximate value of √10 is about 3.162.
So, when you calculate it:
√40 ≈ 2 × 3.162 = 6.324
If we want to express √40 as a fraction, we can write it as:
√40 = 2√10, or approximately 6.324, which can be approximated as the fraction 6324/1000 (simplifying gives us 3162/500).
Hence, while √40 cannot be expressed as a simple fraction, we can represent it in this approximate form.