Algebra Homework help?

Question

x^2 = -1/3

I know you have to take the square root of both sides, but I am not sure how to take the square roots of the negative fraction.

Can someone help me out?

Answer 1

Hi,

To take the square root of a negative number, like -1/3, first split into -1 * 1/3 and replace the square root of -1 with an i outside the radical. That's the symbol for an imaginary number, i, which equals and replaces the square root of -1. Then, besides "i", you have left the square root of 1/3. You don't want to leave a fraction inside a radical, so you multiply both its numerator and denominator by the square root of the denominator, namely by the square root of 3. This makes the numerator just the square root of 3, but the denominator multiplies together to make the square root of 9 which just equals 3 without any radical.

So your answer in simplified form is "i" radical 3 over the number 3.

I hope that helps.

Answer 2

This equation would have imaginary solutions. If you've never talked about imaginary solutions and how to find them in your class, then it's probably ok to say that there are "no real solutions" to this one. Otherwise it would be:

x^2 = -1/3
x = +- the square root of i/3, but then you would have to rationalize the denominator, so the answer would be
+- i(square root of 3)/3

Sorry this is hard to read, but there's no way to write a radical symbol on the computer.

Answer 3

Taking the square root of any negative number results in an imaginary number, i.

The square root of -1/3 is i*sqrt(1/3), which after rationalizing the denominator leaves i*sqrt(3)/3, or (i/3)*sqrt(3)

Answer 4

If you are unfamiliar with what are called 'imaginary numbers' then the best way for you to deal with this problem is to leave the negative under to radical and simplify.

x^2 = -1/3
x = +- sqr -1/3
x = +- 1 / sqr -3 * (sqr -3)/(sqr -3) =
x = -+ (sqr -3) / 3

Note, sqr -1 = i, by convention so
-+ i (sqr 3)/3
would be better.

Answer 5

There is no real number answer to this problem as you won;t be able to get the sqrt of a negative.

there are iamginary answers to this problem involving the use of i.

x = +- sqrt(1/3) i

Answer 6

you cant square anything and make it come out negative unless your dealing with imaginary numbers, is your homework dealing with imaginary numbers?

Answer 7

x^2 = -1/3
x=+/- i(sqrt (1/3)
where i= sqrt(-1)

Answer 8

this is imposible you have to check the things that you've done before getting to this part!

Answer 9

-.577
b/c inverse operations

Answer 10

it's undefined.