# Can You Rationalize The Denominator 3/sqrt - Sqrt?

3   - √3
√6

you need to have a common denominator, so let's make √3 into a fraction of something over √6.  So let's multiply the √3 by (√6/√6).  You can always multiply something by one, since it doesn't change its value.

3    -  √3√6
√6       √6

now we can combine the numerator over the common denominator

3 - √3√6
√6

this is now a ratio.  but let's try to simply it further by multiplying top and bottom by √6

3√6 - √3√6√6
√6√6

3√6 - 6√3
6

√6 - 2√3
2

thanked the writer.
Oddman commented
You can divide out a 3 from numerator and denominator.
Anonymous commented
Oops, it got cut off. There it is.
3/sqrt - sqrt = (3/sqrt)*(sqrt/sqrt) - sqrt
= 3sqrt/6 - sqrt = sqrt/2 - sqrt
= (sqrt - 2sqrt)/2

thanked the writer.
3/(Sqrt - Sqrt)

To rationalize the denominator, multiply top and bottom by the bottom's
conjugate, Sqrt + Sqrt. And the apply formula: (a - b) multiplied by its conjugate (a + b) is equal
to a^2 - b^2, a difference of squares.

=3(Sqrt + Sqrt)/((Sqrt - Sqrt)(Sqrt + Sqrt))
=3(Sqrt + Sqrt)/(6-3)
=3(Sqrt + Sqrt)/3
=Sqrt + Sqrt

Sqrt = 2.45 and Sqrt3 = 1.732/  So putting the values in the above equation you will get

=2.45 + 1.732
=4.182
thanked the writer. 