Question

Is it a real number or not? Give in integer form or round to two decimal places.

Answer 1

Step 1

Given;

$\sqrt[]{-64}$

Required; To determine if it is a real number or not and to give the number in integer form

Step 2

$\text{Note};\text{ }\sqrt[]{-1}=i$$\sqrt[]{-64}=\sqrt[]{-1}\times\sqrt[]{64}$$\sqrt[]{-64}=\sqrt[]{64}i$$\sqrt[]{-64}=8i$

Step 3

Conclude

$\begin{gathered} \sqrt[]{-64}\text{ = 8i in interger form} \\ \text{And } \\ \sqrt[]{-64}\text{ is not a real number because the square root of negative numbers does not exi}st\text{ among the set of }Real\text{ numbers.} \end{gathered}$

it is not a real number because the square root of negative numbers does not exist among the set of }Real\text{ numbers.}$$