Question 1207360
<pre>
Rationalize the denominator. 

Let cr = cube root.

5/(cr(2))

Let me see.

5/(cr(2)) • (cr(2))/(cr(2))

5(cr(2))/(2)

The book's answer is different.

P. S. How do I upload math photos (geometric figures, graphs of functions, etc) on this site? 


When {{{root(n,R)}}} is rationalized, it becomes: {{{root(n, R)}}} * {{{root(n,R^(n - 1))}}}.
{{{matrix(1,1, 5/(root(3,2)))}}}
{{{5(root(3,2^(3 - 1)))/(root(3,2) * (root(3,2^(3 - 1))))}}} ----- Rationalizing denominator by multiplying numerator & denominator by {{{root(3,2^(3 - 1))}}}
{{{highlight_green(matrix(1,3, 5root(3,2^2)/(root(3,2) * (root(3,2^2))), "=", highlight(matrix(1,7, 5root(3,4)/2, or, (5/2)root(3,4),
or, 5(4^(1/3))/2, or, (5/2)(4^(1/3)) )) ))}}}

<font color = red><font size = 4><b>** Note that:</font></font></b> Denominator {{{matrix(1,11, root(3,2) * (root(3,2^2)), 
"=", matrix(2,1, " ", (2^(1/3)) * (2^(2/3))), "=", 2^(1/3 + 2/3), "=", 2^(3/3), "=", 2^1, "=", 2)}}}</pre>