I am supposed to "write each expression with a rational denominator"

Question

1/thesqrootof 3. I follow the book's explanation, until it suggests dividing the sq. root of 3 by the square root of 3 times the square root of three. I do not understand how that reduces to the square root of three divided by three. What happened to the square root signs? How come this is not the square root of nine?

Thanks for your clarification!

Answer 1

rational denominator is a whole number denomiator.

example:

1/sqrt3 = sqrt3/(sqrt3*sqrt3)= sqrt3 /3

your last question; sqrt 9 is 3, a rational number.

One last example

1/(1-sqrt2) multiply numerator and denominor by the conjugate. Look that term up.

1*(1+sqrt2)/[(1-sqrt2)(1+sqrt2)]=
(1+sqrt2)/(1-2)= - (1+sqrt2)

I bet you see something like this very soon.