Question

(8√18+6√24-√72)÷2√6 сколько получится

Answer 1

$(8sqrt{18}+6sqrt{24}-sqrt{72}):2sqrt{6}=(8sqrt{2cdot9}+6sqrt{4cdot6}-sqrt{2cdot4cdot9}):2sqrt{6}=\=(8cdot3sqrt{2}+6cdot2sqrt{6}-2cdot3sqrt{2}):2sqrt{6}=(24sqrt{2}+12sqrt{6}-6sqrt{2}):2sqrt{6}=\=(18sqrt{2}+12sqrt{6}):2sqrt{6}=(9sqrt{2}+6sqrt{6})cdotsqrt{6}=9sqrt{2}cdotsqrt{6}+6sqrt{6}cdotsqrt{6}=\=9sqrt{2}cdotsqrt{2cdot3}+6(sqrt{6})^2=9sqrt{2}cdotsqrt{2}cdotsqrt{3}+6cdot6=9(sqrt{2})^2cdotsqrt{3}+36=\=9cdot2cdotsqrt{3}+36=18sqrt{3}+36$