Rationalise the denominator and simplify 10

Perhaps I should have included the following extra step:

 $\frac{10}{3\sqrt5}\rightarrow\frac{10\sqrt5}{3\times\sqrt5\times\sqrt5}\rightarrow\frac{10\sqrt5}{3\times5}etc$

i.e. you multiply the expression by 1 in the form $\frac{\sqrt5}{\sqrt5}$  Then you multiply the two $\sqrt5$s on the bottom together.

Hope this explains it adequately for you.

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10/3sqrt5

(10/3)/((3sqrt5)/3)=

3.33/sqrt5

3.33²/sqrt5²=

11.11/5

11.11/5=20/9 so

10/3sqrt5=20/9

Like so:  $\frac{10}{3\sqrt5}\rightarrow\frac{10\sqrt5}{3\times5}\rightarrow\frac{2\sqrt5}{3}$

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How does the 3sqrt5 turn to 3*5?