whats the nearest tenth to -61 square root
The Correct Answer and Explanation is:
The square root of -61 is not a real number because the square root of any negative number does not exist within the real number system. However, in the context of complex numbers, the square root of -61 can be expressed as an imaginary number.
To find the square root of -61, we can first express it as:−61=61⋅−1\sqrt{-61} = \sqrt{61} \cdot \sqrt{-1}−61=61⋅−1
The square root of -1 is represented as iii, where iii is the imaginary unit. So, the square root of -61 becomes:−61=61⋅i\sqrt{-61} = \sqrt{61} \cdot i−61=61⋅i
Next, we find the square root of 61. Using a calculator, the square root of 61 is approximately 7.8102. Therefore:−61≈7.8102i\sqrt{-61} \approx 7.8102i−61≈7.8102i
Now, to express this to the nearest tenth, we round 7.8102 to the nearest tenth, which gives us 7.8. Therefore, the square root of -61 to the nearest tenth is:−61≈7.8i\sqrt{-61} \approx 7.8i−61≈7.8i
In summary, the square root of -61 is a complex number, and its value to the nearest tenth is approximately 7.8i7.8i7.8i, where iii denotes the imaginary unit.
