Question

What is the sum of the square root of negative 2 and the square root of negative 18

Answer 1

The sum of the square root of negative 2 and the square root of negative 18 is 4√2i, which is a complex number involving the imaginary unit i.

Step-by-step explanation:

The question asks for the sum of the square root of negative 2 and the square root of negative 18. In mathematics, the square root of a negative number involves the concept of imaginary numbers. Specifically, the square root of -1 is defined as the imaginary unit, denoted by i. Thus:

• √(-2) = √2 × √(-1) = √2 × i
• √(-18) = √18 × √(-1) = √(9×2) × i = 3√2 × i

Now, to find the sum:

√(-2) + √(-18) = √2 × i + 3√2 × i = (1 + 3)√2 × i = 4√2 × i

The sum is 4√2i, which is a complex number.

Answer 2

1. i square root of 2
2. 3i square root of 2