can someone help me

Question

Give an example

Answer 1

Karen,

The expression under the radical sign cannot be negative if you are taking an even numbered root. But it can be negative if you have an odd number root. For example:

√-4 = ??? The answer does not exist. Because 2 * 2 = 4, and -2 * -2 = 4.

There are no two numbers you could multiply to get -4.

Or ⁴√-16 = ??? This answer also does not exist. 2 * 2 * 2 * 2 = 16. And -2 * -2 * -2 * -2 = 16. No number multiplied by itself 4 times (or any EVEN number of times) can ever give you a negative number because the negative signs cancel out.

But what about ³√-27 ?

-3 * -3 * -3 = -27

If you are taking an odd root, such as the third root, then you can have a negative number under the radical sign.

You have to bear this rule in mind when dealing with variables.

For example, ⁸√20x. Can x be negative? No, because we can’t have a negative number under the radical sign when taking an even root.

Or what about ⁴√(3 - x)? Can x be greater than 3? No, because same exact rule: no negatives under the radical sign when taking an even root.

But what about ⁷√(5 - x)? Can x be greater than 5? Sure, because here we have an odd root, so w can totally have a negative under the radical sign.

Hope this helps! :)

Answer 2

The value of the variable under the radical must be equal to or greater than zero.

√-1 is not a real number.