Question

выполните действия
а) $sqrt{15} * sqrt{ frac{1}{125} } * sqrt{27}$
б) $frac{1}{2} sqrt{12} + frac{1}{3} sqrt{48} + frac{1}{4} sqrt{27}$

Answer 1

a)
$sqrt{15}* sqrt{ frac{1}{125} }* sqrt{27}= sqrt{3}* sqrt{5}* frac{1}{ sqrt{25}* sqrt{5} }* sqrt{9}* sqrt{3}= \ \ = sqrt{3}* sqrt{5}* frac{1}{5 sqrt{5} }*3* sqrt{3}=9* frac{1}{5}=1.8$

б) $frac{1}{2} sqrt{12}+ frac{1}{3} sqrt{48}+ frac{1}{4} sqrt{27}= \ = frac{1}{2} sqrt{4}* sqrt{3}+ frac{1}{3} sqrt{16}* sqrt{3}+ frac{1}{4} sqrt{9} *sqrt{3} = \ = frac{1}{2}*2 sqrt{3}+ frac{1}{3}*4 sqrt{3}+ frac{1}{4}*3 sqrt{3}= \ = sqrt{3}(1+ frac{4}{3}+ frac{3}{4} ) = sqrt{3}( frac{12}{12}+ frac{16}{12}+ frac{9}{12} )= frac{37 sqrt{3} }{12}$