How do you simplify 2/(square root of -24)?

Question

Isaiah Anthony · Accepted Answer

#2/sqrt(-24)=1/{sqrt(6)i}# Since the square root of a negative number doesn't exist among the real numbers, you'll have do deal it with complex numbers. In this set, the square root of a negative number equals #i# times the square root of the positive numbers, because #i^2=-1# by definition, and for example you have #sqrt(-25)=sqrt((-1)*25)=sqrt(-1)*sqrt(25)=i*5=5i#. In your case, #sqrt(-24)=sqrt((-1)*24)=sqrt(-1)*sqrt(4*6)=sqrt(-1)*sqrt(4)*sqrt(6)# which thus equals #2sqrt(6)i#. So, #2/sqrt(-24)=2/{2sqrt(6)i}=1/{sqrt(6)i}#, canceling the #2#'s

Eva Abramson · Answer

undefined To simplify 2/(square root of -24), we can start by simplifying the square root of -24. The square root of -24 can be written as the square root of -1 times the square root of 24. The square root of -1 is denoted as "i", representing the imaginary unit. The square root of 24 can be simplified as 2 times the square root of 6. Therefore, the square root of -24 simplifies to 2i times the square root of 6.

Now, substituting this value back into the original expression, we have 2/(2i times the square root of 6). To simplify this further, we can multiply the numerator and denominator by the conjugate of the denominator, which is -2i times the square root of 6.

By doing this, we get (2 times -2i times the square root of 6) / ((2i times the square root of 6) times (-2i times the square root of 6)). Simplifying this expression gives us -4i times the square root of 6 / (-2i times -2i times the square root of 6 times the square root of 6).

Further simplification yields -4i times the square root of 6 / (-2i times -2i times 6).

Finally, simplifying the expression gives us -4i times the square root of 6 / (4 times 6).

This can be further simplified to -i times the square root of 6 / 6.