Simplifying Surd Fractions

Question

can someone show me how to simple surd fractions such as: $$\frac{{8\sqrt 3 }}{2}$$ Can someone please help me here?

Answer 1

Think of that as: $$\frac{1}{2} \cdot 8 \cdot \sqrt{3}$$ But you know that $(1/2) \cdot 8 = 4$, so we get: $$\frac{8\sqrt{3}}{2} = 4\sqrt{3}$$

Answer 2

What I like to do is separate the roots from the integers. Thus, given $$\frac{{8\sqrt 3 }}{2}$$ I like to see it as:

$$\frac{8}2 {\sqrt 3}$$

which we know simplifies to $$4\sqrt 3$$