Question

53. Calcule a medida da diagonal de cada retângulo e classifique o valor obtido em racional ou irracional.
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Answer 1

a)

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

$\mathtt{{d}^{2}={(\sqrt{28})}^{2}+{(\sqrt{8})}^{2}}\\\mathtt{{d}^{2}=28+8=36}\\\mathtt{d=\sqrt{36}=6cm}$

racional.

b)

$2,5=\dfrac{25}{10}=\dfrac{5}{2}$

$\mathtt{{d}^{2}={5}^{2}+{(\dfrac{5}{2})}^{2}}\\\mathtt{{d}^{2}=25+\dfrac{25}{4}=\dfrac{125}{4}}$

$\mathtt{d=\sqrt{\dfrac{125}{4}}=\dfrac{5\sqrt{5}}{2}~cm}$

irracional

c)

$3\sqrt{2}=\sqrt{{3}^{2}.2}=\sqrt{18}$

$\mathtt{{d}^{2}={(\sqrt{18})}^{2}+{(\sqrt{5})}^{2}}\\\mathtt{{d}^{2}=18+5=23}\\\mathtt{d=\sqrt{23}~cm}$

irracional