Question

va rog
Se considera numerele a=(√8+√2)×(√27-√3)si b=√2×(√12+2√75):(√2+2√8-√18).Aratati ca numarul(a√2):b este naturql

Answer 1

a = $( 2\sqrt{2} [tex]+ \sqrt{2}$ )[/tex] × $(3\sqrt{3} - \sqrt{3} )$ = $3\sqrt{2}$ × $2 \sqrt{3} =6 \sqrt{6}$

b = $\sqrt{24}$ + $2\sqrt{150} : ( \sqrt{2} +4 \sqrt{2} -3 \sqrt{2} ) =$ = $(2 \sqrt{6} + 10 \sqrt{6} ): 2\sqrt{2} =12 \sqrt{6} :2 \sqrt{2} =6 \sqrt{3}$

$(a \sqrt{2} ):b = 6\sqrt{12} : 6\sqrt{3} = \sqrt{4} =2$
 
2 ∈ N