Question

Which of the following are irrational numbers

The square root of 41
The square root of 78
The square root of 1
-61

Answer 1

To determine which of the given numbers are irrational, let's analyze each one:

1. **The square root of 41**: The number 41 is not a perfect square (since 6² = 36 and 7² = 49), thus \(\sqrt{41}\) is an irrational number.

2. **The square root of 78**: Similar to 41, 78 is not a perfect square (since 8² = 64 and 9² = 81), thus \(\sqrt{78}\) is also an irrational number.

3. **The square root of 1**: The number 1 is a perfect square (1² = 1), so \(\sqrt{1} = 1\), which is a rational number.

4. **-61**: This is a negative integer and integers are considered rational numbers (any integer can be expressed as a fraction, such as \(-61/1\)).

In summary, the irrational numbers from the list are:

- The square root of 41
- The square root of 78