Expert: Scott A Wilson - 3/19/2010

Question
1. Simplify

(√6)/ √2 + √3

a)1
b)(2√3 - 3√2)
c)(6√2 -√3)
d) (3√2 - 2√3)


2. Simplify:

^3√(2w-5) =1

A)w=7
b)w=16
c)w=3
d)w=-5


3. Solve:

√(n+6) - √n = √6

a) n=3
b)n=0
c)no solution
d)n=-1

Answer
1. Simplify (√6)/ √2 + √3
Note that the first one has √'s in the top and bottom, so it is √(6/2) = √3.
As written, that is √3 + √3 = 2√3.

This doesn't work, so maybe the problem to try is √6/(√2+√3).
Multiply top and bottom by √2 - √3.  This gives (6√2 - 6√3)/(2-3) = 6√3 - 6√2.

a)1
b)(2√3 - 3√2)
c)(6√2 -√3)
d) (3√2 - 2√3)

I don't see that either.


2. Simplify: ^3√(2w-5) = 1

Cube both sides, giving 2w-5 = 1.
Add 5 to both sides, and the divide by 2, giving one of the answers.

A)w=7
b)w=16
c)w=3
d)w=-5


3. Solve: (n+6) - √n = √6

Add √n to both sides.  This gives n + 6 = √n + √6.
Note that the left sides is the sum of the two terms on the right side squared.
Since one of the two terms is 6, and this is far greater than 1, it obviously has no solution.

a) n=3
b) n=0
c) no solution
d) n=-1