Question 237777
3cubed root of 27 + 12 cubed root of 216.
:
 I am going to use {{{3sqrt(n)}}} as a symbol for cube root
:
{{{3*3sqrt(27) + 12*3sqrt(216)}}}
You know the cube root of 27 is 3: (3*3*3=27)
{{{3*3 + 12*3sqrt(216)}}}
:
Factor 216 to reveal some perfect cubes inside the radical 8 * 27 which are 2^3 & 3^3
{{{9 + 12*3sqrt(8*27)}}}
extract the perfect cubes, gets rid of the radical
9 + 12*2*3
9 + 72 = 81
:
to check on a calc use the exponent equiv of cube root ^(1/3)
:
Enter:3*27^(1/3) + 12*216^(1/3) results in 81; confirms your solutions