Question

How do you simplify 2 cubed root 81 + 3 cubed root 24?

Answer 1

The answer is `12root(3)3` and the solution follows.

Explanation:

Look at the values whose cube roots are involved in the problem and determine whether they are perfect cubes or whether they contain factors which are perfect cubes (24 is 3 x 8, and 8 is a perfect cube, and 81 is 3 x 27; 27 is a perfect cube).

This allows you to simplify the problem as shown here:

`2root(3)81+3root(3)24`

`2root(3)(27xx3)+3root(3)(8xx3)`

`2(root(3)(27)xxroot(3)(3))+3(root(3)(8)xxroot(3)(3))`

This step is true because `root(3)(axxb) = root(3)axxroot(3)b`
I've put in some brackets in the hope of keeping this clear.

`2(3xxroot(3)(3))+3(2xxroot(3)(3))`

`6root(3)(3)+6root(3)(3) = 12root(3)3`

Answer 2

`12root(3)3`

Explanation:

`2root(3)81+3root(3)24 =2root(3)27.3+3root(3)8.3`

`=2.3root(3)3+3.2root(3)3= 6root(3)3+6root(3)3 = 12root(3)3`