This problem: sqrt of 3, minus sqrt of one-third. i really need help with it?

Answer 1

The problem is partly that you aren't allowed to have square roots in the denominator, so you have to rationalize the denominator of sqrt(1/3). You can make the sqrt(3) in the denominator go away by multiplying by another sqrt(3), but to keep from changing the fraction's value, you have to multiply by another sqrt(3) in the numerator. So:

sqrt(1/3) = sqrt(1)/sqrt(3) = 1/sqrt(3) =

(1/sqrt(3)) * (sqrt(3)/sqrt(3)) = sqrt(3)/3

So, your problem becomes

sqrt(3) - sqrt(3)/3

The least common denominator is 3, so

sqrt(3) - sqrt(3)/3 =

(3 sqrt(3) - sqrt(3))/3 = 2 sqrt(3)/3

It's kind of hard to see it when you have to write the fractions this way - I hope this helps.

Answer 2

sqrt3=1.732
The sqrt(1/3) is the same as sqrt(1)/sqrt(3) or 1/sqrt3 which is 0.577
subtract that 1.732-0.577=1.154
Because you are dealing with square roots, the answer will also be the square root of something so square 1.154 to find this number: 1.154^2=1.333 so the answer is sqrt(1.333) or sqrt(4/3)

Brian, Diane, and jbljackie's answers will give you the same number because sqrt(4/3)=2sqrt(3)/3=1.1547.

Answer 3

sqr3 -sqr 1/3 = sqr 3-1/3
=sqr 9/3 - 3/3
=sqr 6/3
= sqr 2

Answer 4

3^(1/2) - 3^(-1/2) = 3^(1/2) - (1^(1/2)/3^(1/2))
= 3^(1/2)*3^(1/2)/3^(1/2) - 1/3^(1/2)
= 3/3^(1/2)-1/3^(1/2)
= 2/3^(1/2) = 2(3^(1/2))/3 or (2/3)(3^(1/2)) or (2 sqrt3)/3

Answer 5

1.1547