Expert: Richard J. Raridon - 3/10/2009

Question
31. Simplify: 1 ÷ ^3 sqrt64



32. Simplify: ^3 sqrt48 / sqrt2



33. Simplify: sqrt3 / sqrt4 + sqrt27 / sqrt4



34. Simplify: (sqrt7 - sqrt2)^2



35. Solve for x: sqrt2x + 5 - 1 = x  

Answer
31. I presume by ^3sqrt64 you mean the cube root of 64.  You should write it 64^1/3.  Square roots are written x^1/2
1/(64)^1/3 = 1/4
32. (48^1/3)/(2^1/2) = 2(6^1/2)/(2^1/2) = 2(3^1/2)
33. (3^1/2)/2 +(27^1/2)/2 = (3^1/2)/2 +3(3^1/2)/2 = 2(3^1/2)
34. (7^1/2 -2^1/2)^2 = 7 -28^1/2 +2 = 9 -2(7^1/2)
35. Is that (2x)^1/2 or (2x+5)^1/2 ?