# How do you simplify (5sqrt12+4sqrt147)/sqrt2?

$19 \sqrt{6}$
$\frac{5 \sqrt{12} + 4 \sqrt{147}}{\sqrt{2}} = \frac{5 \cdot \sqrt{2 \cdot 2 \cdot 3} + 4 \cdot \sqrt{7 \cdot 7 \cdot 3}}{\sqrt{2}} = \frac{5 \cdot 2 \cdot \sqrt{3} + 4 \cdot 7 \cdot \sqrt{3}}{\sqrt{2}} = \frac{\sqrt{3} \cdot \left(10 + 28\right)}{\sqrt{2}} = \frac{38 \cdot \sqrt{3}}{\sqrt{2}} = \frac{19 \cdot \sqrt{2} \cdot \cancel{\sqrt{2}} \cdot \sqrt{3}}{\cancel{\sqrt{2}}} = 19 \cdot \sqrt{2} \cdot \sqrt{3} = 19 \sqrt{6}$[Ans]