Question

Simplifique:
a)
$\sqrt{8 } + \sqrt{32} + \sqrt{72} - \sqrt{50} =$
b)
$\sqrt{20} - \sqrt{24} + \sqrt{125} - \sqrt{54} =$
​

Answer 1

Resposta:

Explicação passo a passo:

a)

$\sqrt{8} =\sqrt{2^{3} }=\sqrt{2^{2}.2} =2\sqrt{2}$

$\sqrt{32}=\sqrt{2^{5} } =\sqrt{2^{2}.2^{2}.2 } =2.2\sqrt{2} =4\sqrt{2}$

$\sqrt{72} =\sqrt{2^{3}.3^{2} } =\sqrt{2^{2}.2.3^{2} } =2.3\sqrt{2} =6\sqrt{2}$

$\sqrt{50} =\sqrt{2.5^{2} } =5\sqrt{2}$

Portanto...

$2\sqrt{2} +4\sqrt{2} +6\sqrt{2} -5\sqrt{2} = 7\sqrt{2}$

b)

$\sqrt{20} =\sqrt{2^{2} .5} =2\sqrt{5}$

$\sqrt{24} =\sqrt{2^{3}.3 } =\sqrt{2^{2}.2.3 } =2\sqrt{6}$

$\sqrt{125} =\sqrt{5^{3} } =\sqrt{5^{2}.5 } =5\sqrt{5}$

$\sqrt{54} =\sqrt{2.3^{3} } =\sqrt{2.3^{2}.3 } =3\sqrt{6}$

Portanto...

$2\sqrt{5} -2\sqrt{6} +5\sqrt{5} -3\sqrt{6} =$

$2\sqrt{5} +5\sqrt{5} -2\sqrt{6} -3\sqrt{6} =$

$7\sqrt{5} -5\sqrt{6}$