Question

Calculați modulul numărului real x in fiecare dintre cazurile:

Answer 1

Răspuns:

$a) \: |8 \sqrt{15} - 6 \sqrt{5} \div (3 \sqrt{3} | \div 2 \sqrt{3} = |8 \sqrt{15} - 6 \sqrt{15} \div 3 | \div 2 \sqrt{3} = |8 \sqrt{15} - 2 \sqrt{15} | \div 2 \sqrt{3} = 6 \sqrt{15} \div 2 \sqrt{3 } = 6 \sqrt{30} \div 6 = \sqrt{30}$

$b) \: |40 \sqrt{3} \div ( - 2 \sqrt{5) - 5 \sqrt{15} } | \div 3 \sqrt{3} = | - 20 \sqrt{15} \div 5 - 5 \sqrt{15} | \div 3 \sqrt{3} = | - 4 \sqrt{15} - 5 \sqrt{15} | \div 3 \sqrt{3} = | - 9 \sqrt{15} | \div 3 \sqrt{3} = 9 \sqrt{15} \div 3 \sqrt{3} = 3 \sqrt{15} \div \sqrt{3} = 3 \sqrt{45} \div 3 = \sqrt{45} = 3 \sqrt{5}$

$c) \: | { (- \sqrt{6}) }^{3} + 8 \sqrt{30} \div ( - \sqrt{5} ) | \div ( - 7 \sqrt{3} = | - 6 \sqrt{6} - 8 \sqrt{6} | \div ( - 7 \sqrt{3} ) = |( - 14 \sqrt{6} | \div ( - 7 \sqrt{3} ) = - ( - 14 \sqrt{6} ) \div - 7 \sqrt{3} = 2 \sqrt{6} \div \sqrt{3} = 2 \sqrt{18} \div 3 = 6 \sqrt{2} \div 3 = 2 \sqrt{2}$

$d) \: ( - 6 \sqrt{3} ) \div |(3 \sqrt{42}) \div ( - \sqrt{7)} - {( - \sqrt{6} }^{3} | = ( - 6 \sqrt{3} ) \div |( - 3 \sqrt{294} \div 7 + 6 \sqrt{6} | = ( - 6 \sqrt{3} ) \div | - 21 \sqrt{6} + 6 \sqrt{6} | = ( - 6 \sqrt{3} ) \div | - 15 \sqrt{6} | = ( - 6 \sqrt{3} \div 15 \sqrt{6} = - 6 \sqrt{18} \div 15 \times 6 = - 3 \sqrt{2} \div 15 = - \sqrt{2} \div 5$