radical question?

Question

simplify

(radical sign) -4/7

Answer 1

√ (-4/7) = 2 i / √ 7 = 2/7 i √ 7

Answer 2

Okay. I'm going to use the notation sqrt(-4/7), okay?

First, we notice that the term under our root is negative. This means we can pull out an i. So now we have,

i * sqrt(4/7)

We see that while 4/7 ISN'T a perfect square, one term in the fraction (4) is. So we want to rewrite the equation using one of our exponent rules:

i * (sqrt(4) / sqrt(7))

Now we know that the sqrt(4) is 2. So we can rewrite again as:

2i / sqrt(7).

Now technically, you're done. But in math books, they don't like having square roots on the bottom of a fraction which means we want to RATIONALIZE. To do this, we multiply top and bottom of the fraction by sqrt(7) [the denominator]. Doing this yields:

[2i / sqrt(7)] * [sqrt(7) / sqrt(7)]
= [2i*sqrt(7)] / [sqrt(7) * sqrt(7)]

Remember that any square root times itself just disappears. So sqrt(7) * sqrt(7) is just 7. Thus, we can simplify for the last time as:

2i*sqrt(7) / 7

That's the simplest form.

Answer 3

Hello,

The square root of -4 is -2i Sqrt (1/7) now multiply both top and bottom of the radical by 7 giving us -2iSqrt(7/49) then take out the 49 on the bottom and we have -2i/7 sqrt7.

Hope This Helps!

Answer 4

sqrt( -4/7)

Note that i^2 =-1

-4/7 = (-1)(4/7) = (i^2)(4/7)

sqrt(-4/7) = 2i /(sqrt(7)) or 2i sqrt(7)/7

This can be further simplified if you want to

using the fact that any complex number x +iy
can be written in the following form

x +iy = r e ^(i theta), where

r = sqrt ( x^2 + y^2)

x +iy = r (cos(theta) + i sin(theta)).

cos (theta) = x/r ; sin(theta) = y/r

and you continue.

in our example our complex number is 2i sqrt(7)/7

here x = 0 and y = 2 sqrt(7)/7
you find theta and r
write 2i sqrt(7)/7 = r e^(i theta)

Good luck !!!