Can someone show me how to figure this out: √-40 / √-8?

Answer 1

Complex numbers

sqrt-40 = sqrt40*sqrt-1
sqrt-8 = sqrt8*sqrt-1

=(sqrt40)i/(sqrt8)i
=sqrt40/sqrt8

=sqrt 5

Answer 2

Just divide through

40/8 = 5

so the answer is square root of 5

Answer 3

The square root of 5.

You can not take the square root of a negative number. You may have an i (imaginary number) in the somewhere.

The i's may cancel, since there is one on the top and one on the bottom.

Answer 4

We cannot take the square root of a negative number.

So, we say sqrt{-1} = i

Our numerator is:

sqrt{-40} which becomes sqrt{4} times the sqrt{10} times i

We now have this in the numerator:

2i(sqrt{10})

Let's now do the denominator.

We have sqrt{-8}, which becomes sqrt{4} times sqrt{2} times i

Here is our new denominator:

4i(sqrt{2})

Our new fraction is:

2i(sqrt{10})/4i(sqrt{2})

Let's reduce the 2i/4i first.

2i/4i = 1/2

We now have:

1(sqrt{10}) divided by 2(sqrt{2})

We cannot have a radical in the denominator.

So, we have to RATIONALIZE the denominator.

1(sqrt{10}) times 2(sqrt{2})
------------------------------------- = sqrt{20}/2
2(sqrt{2}) times 2(sqrt{2})

The square root of 20 can be broken down further and it becomes 2(sqrt{5}) as our new numerator.

We now have this fraction:

2(sqrt{5})/2

Both number 2's cancel each other out leaving us with the answer sqrt{5}, which is read: "The square root of 5."

Answer 5

√-40/√-8=√(-40/-8)=√(5)