Question

4. find the real number roots. sqrt-0.25

Answer 1

Given is square root of a negative real number, i.e. $\sqrt{-0.25}$

When we find square root of positive real numbers, we get Real answers.

But when we find square root of negative real numbers, we get Imaginary answers. To solve them, we can split the given negative number into product of -1 and the number itself but with positive sign. e.g. -4 = -1 x 4.

For square root of -1, we use english letter 'i' called Imaginary unit i.e. $\sqrt{-1} = i$

Now we can use -0.25 = -1 x 0.25

$\sqrt{-0.25} =\sqrt{-1*0.25} \\\\ \sqrt{-0.25} =\sqrt{-1}*\sqrt{0.25} \\\\ \sqrt{-0.25} =i*0.5 \\\\ \sqrt{-0.25} =0.5i$

Hence, "0.5i" is the final answer.

Answer 2

You can find real numbers root. It would be Undefined