Expert: Scott A Wilson - 4/6/2010

Question
1. simplify:
The square root of 3 to the square root of 2 power times the square root of 3 to the negative square root of 2 power.

a)3^-1
b)1/3
c)1
4)3


2. simplify:
The square root of 2 to the square root of 2 power all to the square root of 2 power.

a)4
b)2
c)4 to the square root of 2 power
d)-2


3. simplify:
(The square root of 2 minus 1 to the 2 plus y power) all divided by (the square root of 2 minus 1 to the y power).

a)2^1/2
b)3 - 2(2^1/2)
c)1
d)3+2(2^1/2)


4.simplify:
The square root of 2 to the negative 9 plus 3 power

a) 2 square root of 3 divided by 2
b)8
c)1/2
d)1/8

Answer
1. simplify: The square root of 3 to the square root of 2 power times the square root of 3 to the negative square root of 2 power.

That is, (√3^√2)(√3^-√2) = √3^(√2-√2) = √3^0 = 1, and that's one of the choices.

a)3^-1; b)1/3; c)1; 4)3


2. simplify: The square root of 2 to the square root of 2 power all to the square root of 2 power.

Note that when we have (a^b)^c, it is the same as a^(bc).
Here, b and c are both √2, so bc is 2, so the answer is √2², and that is 2.


3. simplify:
(The square root of 2 minus 1 to the 2 plus y power) all divided by (the square root of 2 minus 1 to the y power).

That is, [(√2 - 1)^(2+y)]/[(√2 - 1)^y], which become (√2 - 1)^(2+y-y).
That is the same as (√2 - 1)² = 4 - 2√2 + 1 = 5 - 2√2.

It looks like whoever wrote the test computed (√2 - 1)² as 4 - 2√2 - 1, which is (b) 3 - 2√2,
however, that is incorrect, since the -1 should be a + 1.

a)2^1/2; b)3 - 2(2^1/2); c)1; d)3+2(2^1/2)


4.simplify: The square root of 2 to the negative 9 plus 3 power

That is (√2)^(-9+3) = √2^(-6) = 1/√2^6 = 1/2^3 = 1/8, and that's there as well.

a) 2 square root of 3 divided by 2; b)8; c)1/2; d)1/8