# Question #15e2b

Oct 21, 2017

${9}^{3} \sqrt{5} - {6}^{3} \sqrt{5} = 513 \sqrt{5}$

#### Explanation:

First of all, let's review what we know about subtracting square root expressions with the same radicand:

$a \sqrt{b} - c \sqrt{b} = \left(a - c\right) \sqrt{b}$

With this in mind,

${9}^{3} \sqrt{5} - {6}^{3} \sqrt{5} = \left({9}^{3} - {6}^{3}\right) \sqrt{5}$

Aha! Now, by doing some computation, we can figure out that

${9}^{3} - {6}^{3} = 513$

$513 \sqrt{5}$