# How do you evaluate 2√3 3√5 - 4√5?

$6 \sqrt{15} - 4 \sqrt{5}$
The equation can be rewritten as $\left(2 \sqrt{3} \cdot 3 \sqrt{5}\right) - 4 \sqrt{5}$.
$a \sqrt{b} \cdot c \sqrt{d} \equiv \left(a \cdot c\right) \sqrt{b \cdot d}$, so $2 \sqrt{3} \cdot 3 \sqrt{5} = \left(2 \cdot 3\right) \sqrt{3 \cdot 5} = 6 \sqrt{15}$.
You now have $6 \sqrt{15} - 4 \sqrt{5}$, as 15 has no factors which are perfect squares, $6 \sqrt{15}$ cannot be simplified further, leaving you with $6 \sqrt{15} - 4 \sqrt{5}$.