Question

Resolva a expressão numérica:

$\mathsf{\left(\dfrac{4}{9}\right)+\left[\left(\dfrac{5}{2}\right)^2-\left(\sqrt{\dfrac{160}{81}+\dfrac{1}{9}}\right)\right]=\,?}$​

Answer 1

5,25

Explicação passo-a-passo:

Aritmética,

$\mathsf{\left(\dfrac{4}{9}\right)+\left[\left(\dfrac{5}{2}\right)^2-\left(\sqrt{\dfrac{160}{81}+\dfrac{1}{9}}\right)\right]} \\ \mathsf{\left(\dfrac{4}{9}\right)+\left[\left(\dfrac{ {5}^{2} }{ {2}^{2} }\right)-\left(\sqrt{\dfrac{160}{81}+\dfrac{1 \times 9}{9 \times 9}}\right)\right]} \\ \mathsf{\left(\dfrac{4}{9}\right)+\left[\left(\dfrac{25}{4}\right)-\left(\sqrt{\dfrac{160 + 9}{81}}\right)\right]} \\ \mathsf{\left(\dfrac{4}{9}\right)+\left[\left(\dfrac{25}{4}\right)-\left({\dfrac{ \sqrt{169} }{ \sqrt{81} }}\right)\right]} \\\mathsf{\left(\dfrac{4}{9}\right)+\left[\left(\dfrac{25}{4}\right)-\left({\dfrac{ {13} }{ {9} }}\right)\right]} \\\mathsf{\left(\dfrac{4}{9}\right)+\left(\dfrac{25}{4}\right)-\left({\dfrac{ {13} }{ {9} }}\right)} \\ \frac{4}{9} + \frac{25}{4} - \frac{13}{9} \\ \frac{4 \times 4}{9 \times 4} + \frac{25 \times 9}{4 \times 9} - \frac{13 \times 4}{9 \times 4} \\ \frac{16 + 225 - 52}{36} \\ \frac{189}{36} \\ \frac{63}{12} \\ \frac{21}{4} \\ 5.25$

Espero ter ajudado.

Answer 2

Resposta:

$\frac{21}{4}$

Explicação passo-a-passo:

$\frac{4}{9} + (( \frac{5}{9})^{2} - \sqrt{ \frac{161}{81} } + \frac{1}{9} ) \\ \\ \frac{4}{9} + ( \frac{25}{4} - \sqrt{ \frac{160}{81} } + \frac{1}{9} ) \\ \\ \frac{4}{9} + ( \frac{25}{4} - \sqrt{ \frac{169}{81} } ) \\ \\ \frac{4}{9} + ( \frac{25}{4} - \frac{13}{9} ) \\ \\ \frac{4}{9} + \frac{173}{36} \\ \\ \frac{21}{4}$

$\Large\mathscr{\red{Attard}}$