Question

How do you simplify $\sqrt{-50}$ ?

Answer 1

Hint: We know that square root of -1 is equal to i , we know that $\sqrt{ab}$ is equal to $\sqrt{a}\sqrt{b}$ . so we can apply this formula to $\sqrt{-50}$ and write $\sqrt{-50}$ = $\sqrt{50}\sqrt{-1}$ . we know square root of -1 is i , so now we can solve for $\sqrt{-50}$ .

Complete step by step solution:
We have to evaluate $\sqrt{-50}$ , we know that $\sqrt{ab}$ is equal to $\sqrt{a}\sqrt{b}$ .
We know that square root of – 1 is denoted by imaginary number I, that means square of i is equal to -1.
So $\sqrt{-50}$ is equal to $\sqrt{50}\sqrt{-1}$ , square root of – 1 is equal to i . so we can write
$\Rightarrow \sqrt{-50}=i\sqrt{50}$
$\Rightarrow i5\sqrt{2}$
So for any positive number m, the value of $\sqrt{-m}$ is equal to $i\sqrt{m}$ .
Since square of i is equal to -1 , cube of i is equal to
$\Rightarrow {{i}^{3}}=i\times {{i}^{2}}=-i$
Similarly ${{i}^{4}}=i\times {{i}^{3}}$
$\Rightarrow {{i}^{4}}=i\times -i=1$
Then it will repeat for 5, 6 and so on.
We can represent any complex number in the cartesian plane where the x axis is the real part and y axis the imaginary part.
The angle between the positive x axis and the straight line joining the point and origin is known as argument. Real number lies on the x axis and the purely complex number lies on y axis.

Note: Most people make mistakes in the definition of complex numbers. Complex number is any number that can be represented as a + ib where a is the real part and b is the complex part. Keep in mind that all real numbers are complex numbers, but not all complex numbers are real numbers. The complex number which has imaginary part 0 are real. So we can say that complex numbers are the superset of real numbers, rational numbers, irrational numbers.