Question

Resolva as expressões.

Answer 1

Resposta:

Solução:

a)

$\sf \displaystyle \left ( \sqrt{18} + \sqrt{98} + \sqrt{200} \right ) \div \left ( 2\sqrt{2} + \sqrt{8} \right ) =$

$\sf \displaystyle \left ( \sqrt{9 \cdot 2} + \sqrt{49 \cdot 2} + \sqrt{100 \cdot 2 } \;\right )\div \left ( 2\sqrt{2} + \sqrt{4 \cdot 2} \right ) =$

$\sf \displaystyle \left ( 3\sqrt{2} + 7\sqrt{2} + 10\sqrt{2} \right) \div \left ( 2\sqrt{2} + 2\sqrt{2} \right ) =$

$\sf \displaystyle \left ( (3 +7 +10) \sqrt{2} \right ) \div \left ( (2+2)\sqrt{2} \right ) =$

$\sf \displaystyle \left ( 20 \sqrt{2} \right ) \div \left ( 4 \sqrt{2} \right ) = \boldsymbol{ \sf \displaystyle 5 }$

b)

$\sf \displaystyle \left ( 10\sqrt{27} + 10\sqrt{3} \right ) \div 10\sqrt{3} =$

$\sf \displaystyle \left ( 10\sqrt{9 \cdot 3} + 10\sqrt{3} \right ) \div 10\sqrt{3} =$

$\sf \displaystyle \left ( 10 \cdot 3\sqrt{3} + 10\sqrt{3} \right ) \div 10\sqrt{3} =$

$\sf \displaystyle \left ( (30 + 10 )\sqrt{3} \right ) \div 10\sqrt{3} =$

$\sf \displaystyle 40 \sqrt{3} \div 10\sqrt{3} = \boldsymbol{ \sf \displaystyle 4 }$

c)

$\sf \displaystyle \left ( 20\sqrt{10} + 10\sqrt{18} \right ) \div 2\sqrt{2} =$

$\sf \displaystyle \left ( 20\sqrt{10} + 10\sqrt{9 \cdot 2} \right ) \div 2\sqrt{2} =$

$\sf \displaystyle \left ( 20\sqrt{10} + 10 \cdot 3\sqrt{2} \right ) \div 2\sqrt{2} =$

$\sf \displaystyle \left ( 20\sqrt{10} + 30\sqrt{2} \right ) \div 2\sqrt{2} =$

$\sf \displaystyle \dfrac{\diagup\!\!\!{ 20}\sqrt{10} }{\diagup\!\!\!{ 2}\sqrt{2} } + \dfrac{\diagup\!\!\!{ 30} \diagup\!\!\!{ \sqrt{2}} }{\diagup\!\!\!{ 2} \diagup\!\!\!{ \sqrt{2}} } =$

$\sf \displaystyle \dfrac{ 10 \sqrt{10} }{\sqrt{2} } \cdot \frac{\sqrt{2} }{\sqrt{2} } + 15 =$

$\sf \displaystyle \dfrac{ 10 \sqrt{20} }{\sqrt{4} } + 15 =$

$\sf \displaystyle \dfrac{ 10 \sqrt{4 \cdot 5} }{2 } + 15 =$

$\sf \displaystyle \dfrac{ 10 \cdot \diagup\!\!\!{ 2} \sqrt{ 5} }{\diagup\!\!\!{ 2} } + 15 =$

$\boldsymbol{ \sf \displaystyle 10 \sqrt{5} + 15 }$

Explicação passo-a-passo: