Calcula o valor exato
Números reais: Matematicamente Falando 8 - Pág. 33 Ex. 4
Ennciado
Calcula o valor exato de:
- \(\sqrt 3 \times \left( {1 + \frac{3}{{\sqrt 3 }}} \right)\)
- \({\left[ {{{\left( {\sqrt 5 } \right)}^2}} \right]^2}\)
- \(\frac{{7\pi – 3\pi }}{{2\pi }} \times \frac{{{{\left( {6\pi } \right)}^2}}}{{2\pi }}\)
Resolução
Calcula o valor exato de:
-
\(\sqrt 3 \times \left( {1 + \frac{3}{{\sqrt 3 }}} \right)\)
-
\({\left[ {{{\left( {\sqrt 5 } \right)}^2}} \right]^2}\)
-
\(\frac{{7\pi – 3\pi }}{{2\pi }} \times \frac{{{{\left( {6\pi } \right)}^2}}}{{2\pi }}\)
- \(\sqrt 3 \times \left( {1 + \frac{3}{{\sqrt 3 }}} \right) = \sqrt 3 + \frac{{3\sqrt 3 }}{{\sqrt 3 }} = \sqrt 3 + 3\)
- \({\left[ {{{\left( {\sqrt 5 } \right)}^2}} \right]^2} = {\left( 5 \right)^2} = 25\)
- \[\frac{{7\pi – 3\pi }}{{2\pi }} \times \frac{{{{\left( {6\pi } \right)}^2}}}{{2\pi }} = \frac{{\left( {7 – 3} \right)\pi }}{{2\pi }} \times \frac{{36{\pi ^2}}}{{2\pi }} = \frac{{4\pi }}{{2\pi }} \times \frac{{36{\pi ^2}}}{{2\pi }} = 2 \times 18\pi = 36\pi \]
