Question 711333
If
{{{root(3, 2)(root(3, 4)-2*root(3, 32))}}}
is the correct expression then please post it as:
(cube root of 2)((cube root of 4) subtract (2 times the cube root of 32))
The extra parentheses make it clear. Without them
cube root of 2(cube root of 4 subtract 2 times the cube root of 32)
could be interpreted as:
{{{root(3, 2*root(3, 4 - 2*root(3, 32)))}}}<br>
If
{{{root(3, 2)(root(3, 4)-2*root(3, 32))}}}
is not correct then you will have to re-post your question because I'm going to simplify this expression.<br>
We could start with either using the Distributive Property to multiply by the {{{root(3, 2)}}} or we could simplify {{{root(3, 32)}}} since 8 is a factor of 32 and 8 is a perfect cube ({{{8 = 2^3}}}). Looking ahead I can see that using the Distributive Property first will make the rest much easier. So that is how I will start:
{{{root(3, 2)*root(3, 4)-root(3, 2)*2*root(3, 32))}}}
Multiplying the roots together, using the {{{root(a, p)*root(a, q) = root(a, p*q)}}} property of radicals we get:
{{{root(3, 2*4)-2*root(3, 2*32))}}}
Simplifying inside the radicals we get:
{{{root(3, 8)-2*root(3, 64))}}}
8, as was mentioned earlier, is a perfect cube. And so is 64! {{{64 = 4^3}}}. So both cube roots simplify:
{{{2-2*4}}}
Continuing to simplify:
{{{2-8}}}
{{{-6}}}