Question

Root 2 root-3 equals to
A.Root 6
B.\[i\] root 6
C.– root 6
D.None of these

Answer 1

Hint: The very basic step we would do will be converting the word problem into algebraic terms. Like the root should be symbolised. Then we know that the negative under root is an imaginary number i. so we will replace that also. And that would be the final answer.

Complete step-by-step answer:
Given that, Root 2 root-3
This can be written as, \[\sqrt 2 .\sqrt { - 3} \]
Now we will start evaluating. The second root can be written as,
\[ = \sqrt 2 \sqrt {3 \times \left( { - 1} \right)} \]
Now we will separate the roots as,
\[ = \sqrt 2 .\sqrt 3 .\sqrt { - 1} \]
We know that, \[\sqrt { - 1} = i\]
\[ = \sqrt 2 .\sqrt 3 .i\]
Now since both are under root we can multiply them as,
\[ = i\sqrt {2 \times 3} \]
Taking the product,
\[ = i\sqrt 6 \]
This can be read as, \[i\] root 6
root 2 root-3 =\[i\] root 6
Thus option 2 is the correct option.
So, the correct answer is “Option B”.

Note: Note that the options are almost closer to each other. The first option has root 6 in it but not the imaginary part. So that is not our answer. In the third option they have given a minus sign of \[\sqrt { - 1} \] considering that the root of 1 will be 1, but that is not the case. \[\sqrt { - 1} = i\] is an imaginary number.
We observe that \[x + iy\] is called a complex number with x as the real part and y as the imaginary part.