Question

Which is equivalent to √3/√8 when denominator is "rationalized"?

Answer 1

Explanation:

`(\sqrt3)/(\sqrt8)=(\sqrt3\cdot\sqrt2)/(\sqrt8\cdot\sqrt2)=(√(3\cdot2))/(√(8\cdot2))=(\sqrt6)/(√(16))=(\sqrt6)/(4)`

Used:

`√(ab)=√(a)\cdot√(b)\ \text{for}\ a\geq0\ \wedge\ b\geq0\\\\√(a)=b\iff b^2=a\ \text{for}\ a\geq0\ \wedge\ b\geq0\\\\√(16)=4\ \text{because}\ 4^2=16`