Question

What is the sum of the √-2 and √-18?

Answer 1

The sum is 4 i√2

Explanation:

Both the numbers √-2 and √-18 are imaginary number and thus can be presented as

i√2 and i√18

On simplifying, the i√18 can be written as i√( 9 x 2)

Taking out square root of 9 we get-

3i√2

Thus the summation of i√2 and i√18 can be written as

i√2 + 3i√2

= 4 i√2

Answer 2

The correct answer is (4 √2) i

Explanation:

The sum we are looking is "x"

x= √-2+ √-18

By the Radical Properties of Multiplication ,

x=√-2 +√(-2*9)

x=√-2 +√-2* √9

Considering √-2= √((-1)*2)= √-1 *√2

According to the propriety of complex numbers , we can say

i=√-1

Replacing

x= i √2 + 3 i√2

The answer is x= (4 √2) i