how do you simplify the expression square root of 1/2 minus square root of 1/8?

Question

√½-√1/8

Answer 1

a square root can also be written as the square root going to the top and bottom separately, you can re-write your problem as: v1/ v2 - v1/ v8 v1 = 1 v2 = v2; cannot be simplified v8 = v2x4 = 2v2 Now you have 1/ v2 - 1/ 2v2 You need to have a common denominator in order to subtract, both have v2 in them, but you are going to have to multiply the first by 2/2 to get the common. Remember you have to multiply the top and bottom of a fraction by the same number when you are trying to get to a common denominator, otherwise you are changing the value of the fraction (2/2)(1/ v2) - 1/ 2v2 = 2/ 2v2 - 1/ 2v2 = or (2-1) / 2v2 1/ 2v2 Most teachers will want you to rationalize your denominator (make sure there are no roots on the bottom half of the fraction). You do this by simply multiplying the whole fraction by the root over itself. For this problem you will multiply by v2/v2 (1/ 2v2)( v2/v2) = (1 x v2) / (2v2 x v2) 1 x v2 = v2 2v2 x v2 = 2v4 = 2 x 2 = 4 Put them back together: v2 /4 Answer: v2 /4