The first thing we need to do is to multiply both numerator and denominator by [tex] \sqrt{3} [/tex] so that the denominator is not a radical any more:
thus, we have [tex]\displaystyle{ \frac{ \sqrt{10} }{ \sqrt{3}} \cdot \frac{ \sqrt{3} }{ \sqrt{3}}= \frac{ \sqrt{10} \cdot \sqrt{3} }{( \sqrt{3} )^2} [/tex].
Now, applying the rules (i) [tex] \sqrt{ x^{2} }=x[/tex] (for x≥0) and (ii) [tex] \sqrt{a} \cdot \sqrt{b} = \sqrt{ab} [/tex], we have:
[tex]\displaystyle{ \frac{ \sqrt{10} \cdot \sqrt{3} }{( \sqrt{3} )^2}= \frac{ \sqrt{30} }{3} [/tex].
Answer: [tex]\displaystyle{ \frac{ \sqrt{30} }{3}[/tex]
