How do you divide $\frac{8 \sqrt{6}}{2 \sqrt{3}}$ $(8sqrt6)/(2sqrt3)$ ?

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Answer 1 · 2018-03-04T14:17:22

$4 \sqrt{2}$ $4sqrt(2)$

We must use our knowledge of surds:

$\sqrt{a \cdot b} = \sqrt{a} \cdot \sqrt{b}$ $sqrt(a*b) = sqrt(a)*sqrt(b)$

$\Rightarrow \sqrt{6} = \sqrt{2 \cdot 3} = \sqrt{2} \cdot \sqrt{3}$ $=> sqrt(6) = sqrt(2*3) = sqrt(2) * sqrt(3)$

$\frac{8 \sqrt{6}}{2 \sqrt{3}} = \frac{8 \sqrt{2} \cdot \sqrt{3}}{2 \sqrt{3}}$ $(8sqrt(6))/(2sqrt(3)) = (8sqrt(2)*sqrt(3))/(2sqrt(3) )$

We can cancel out the $\sqrt{3}$ $sqrt(3)$ as on both numerator and denominator:

$(8sqrt(2)*cancel(sqrt(3)))/(2cancel(sqrt(3) ) ) = (8sqrt(2) )/ 2$

We know $8/2 = 4$

$=> 4sqrt(2)$

How do you divide (8sqrt6)/(2sqrt3)8√62√3(8sqrt6)/(2sqrt3)?