radical sums

Question

whats the sum of the square root of -2 and the square root of -18

Answer 1

Hi Beth.  Here is how to approach the problem:

 

√-2 = √-1 * √2 = i * √2 = √2i

 

√-18 = √-1 * √18 = √-1 * √9 * √2 = 3√2i

 

Thus the sum would be √2i + 3√2i = 4√2i

 

Please note that I am making an important assumption.  Can you tell me what that is?

 

If you have any questions please feel free to post a response.

Answer 2

Mathematicians nicknamed the square root of a negative number, for example, √-1 as  i and created the complex numbers, which all come from that little i.

 

√-2 = √2. √-1 = i√2

√-18= √18.√-1=√18i =  √2..3.3.i= 3i √2

 

the sum of the square root of -2 and the square root of -18 is i√2+3i √2 = 4i√2 or 4√2i