Question

Please show work!!!!!!

Answer 1

Answer:

$\frac{4\sqrt{5} }{5}$

Step-by-step explanation:

Rationalise the denominator by multiplying both the numerator and denominator by $\sqrt{30}$, that is

$\frac{4\sqrt{6} }{\sqrt{30} }$ × $\frac{\sqrt{30} }{\sqrt{30} }$

= $\frac{4\sqrt{180} }{30}$

= $\frac{4\sqrt{36(5)} }{30}$

= $\frac{4(6)\sqrt{5} }{30}$

= $\frac{24\sqrt{5} }{30}$

= $\frac{4\sqrt{5} }{5}$

Answer 2

Answer:

$\frac{4\sqrt{5} }{5}$

Step-by-step explanation:

$\frac{4\sqrt{6} }{\sqrt{30} } =\frac{\sqrt{30} *4*\sqrt{6} } \sqrt{30} {\sqrt{30} }$

$\frac{4\sqrt{6*30} }{30} =\frac{4*\sqrt{180} }{30} =\frac{4*\sqrt{36*5} }{30} = \\\\\frac{4*6\sqrt{5} }{6*5} =\frac{4\sqrt{5} }{5}$