Question

square root of -3 times square root of 12what is the answerJust have to simplify the expression. The exercise provides it in numerical form.

Answer 1

Given the expression:

$\sqrt[]{-3}\cdot\sqrt[]{12}$

You need to remember the following property:

$\sqrt[n]{b^{}}\cdot\sqrt[n]{a}=\sqrt[n]{ba}$

Where "n" is the index of the root and "b" and "a" are Radicands.

Then, since the roots given in the exercise are the same, you can multiply the Radicands:

$=\sqrt[]{(-3)(12)}=\sqrt[]{-36}$

Notice that the number inside the square root is negative. Then, you need to remember the following:

$\sqrt[]{-1}=i$

Therefore, in order to simplify it, you need to take the square root of 36 and write the Imaginary Unit "i" next to it:

$=6i$

Hence, the answer is:

$=6i$