Question

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Answer 1

Explicație pas cu pas:

d)

$= \dfrac{1}{16} : \sqrt{ \dfrac{1}{ {4}^{2} } } - \dfrac{1}{7} \cdot \sqrt{ \dfrac{1225}{100} } + \dfrac{5}{4}$

$= \dfrac{1}{16} : \dfrac{1}{4} - \dfrac{1}{7} \cdot \sqrt{ \dfrac{ {35}^{2} }{ {10}^{2} } } + \dfrac{5}{4}$

$= \dfrac{1}{16} \cdot 4 - \dfrac{1}{7} \cdot \dfrac{35}{10} + \dfrac{5}{4} = \dfrac{1}{4} - \dfrac{1}{2} + \dfrac{5}{4}$

$= \dfrac{1 - 2 + 5}{4} = \dfrac{4}{4} = 1$

a)

$= \dfrac{3}{ \sqrt{2} } - \dfrac{ \sqrt{9} }{ \sqrt{32} } + \dfrac{ \sqrt{49} }{ \sqrt{8} } - \dfrac{ \sqrt{25} }{ \sqrt{2} }$

$= \dfrac{3}{ \sqrt{2} } - \dfrac{3}{ 4\sqrt{2} } + \dfrac{7}{ 2\sqrt{2} } - \dfrac{5}{ \sqrt{2} }$

$= \dfrac{12}{ 4\sqrt{2} } - \dfrac{3}{ 4\sqrt{2} } + \dfrac{14}{ 4\sqrt{2} } - \dfrac{20}{4 \sqrt{2} }$

$= \dfrac{12 - 3 + 14 - 20}{ 4\sqrt{2} } = \dfrac{3}{ 4\sqrt{2} } = \dfrac{3 \sqrt{2} }{8}$