Okay, square root of fractions help?

Question

The problem is the square root of 6/7. Our teacher tought us to simplify the 6, so it would be 2 times the root of 3/7. Then multipy by 7/7. Then to simplify. Am I doing it right? Did I just not understand what he said? He said that since the denominator can't have a square root you have to multiply by 1. (7/7) So I just need to know if i'm doing it right. :) Thanks. ;D

Answer 1

You multiply by the SQUARE ROT of 7 (the denom) on the top and bottom, this is called "rationalizing the denominator" to clear that illegal sqrt on the bottom.

You'd get 6sqrt7/7

You can't split up the 6 in any way, it is already relatively prime the way it is.

Answer 2

√(6/7)

all you can do is get the √7 out of the denominator.

√(6/7) * √(7/7)

√42 / √49

√42 / 7

that's all you can do.

PS √6 is NOT equal to 2√3

√12 = √(4*3) = 2√3

.

Answer 3

the square root of a fraction is the square root of the top divided by the square root of the bottom. that is rule number 1. in algebra:

sqr( a / b ) = sqr(a) / sqr(b)

Now, if sqr(b) happens to be a nice number, good for you. But chances are it won't. Whether you need to "rationalize" the denominator is up to the instructor. My own pre calc teacher didn't care, because it's still the right answer. But to rationalize the denominator, you need to make it so there is no root in the denominator. So, you simply multiply the bottom by itself.

sqr(b) * sqr(b) = b

So, in order to keep it the same, you must also multiply the top. Thus, to please everyone:

sqr(a / b) = sqr(a) / sqr(b) = sqr(a) * sqr(b) / b