Answer
${\frac{3 \sqrt {10}}{2}}$
Work Step by Step
First, we write both numbers in the numerator under the same radical:
$\frac{\sqrt {3} • \sqrt {15}}{\sqrt {2}} = \sqrt {\frac{3 • 15}{2}}$
Multiply what is under the radical sign first:
$\sqrt {\frac{45}{2}}$
Rationalize the fraction by multiplying both the numerator and denominator by $\sqrt 2$:
$\sqrt {\frac{45}{2}} • \frac{\sqrt 2}{\sqrt 2}$
Multiply to simplify:
${\frac{\sqrt {45} • \sqrt 2}{2}}$
Multiply the terms in the numerator:
${\frac{\sqrt {90}}{2}}$
Rewrite $90$ as the product of a perfect square and another number:
${\frac{\sqrt {9 • 10}}{2}}$
Take the square root of $9$ to move it out from under the square root sign:
${\frac{3 \sqrt {10}}{2}}$
