Question

Simplique a seguintes expressões

Answer 1

Resposta:

Vamos lá! Usaremos o método de racionalização de de denominadores nesses pequenos probleminhas.

• Simplifique os radicais sempre que possível pra facilitar os cálculos.

Letra (a)

$\dfrac{5^{2} .5^{8} }{\sqrt{5} .\sqrt{5} } =\dfrac{25 .5^{8} }{(\sqrt{5}) ^{2} }=\dfrac{25.5^{8} }{5} =5.5^{8} =5^{9}$

Letra (b)

$\dfrac{(5^{2})^{2} -106 }{\dfrac{1}{\sqrt{3} } } +\dfrac{3^{2} .2^{2} }{\dfrac{\sqrt{75} }{\sqrt{3} } +\sqrt[3]{3} .\sqrt[3]{9} }= \\\\\\\dfrac{(5^{4})-106 }{\dfrac{1}{\sqrt{3} } } +\dfrac{9 .4 }{{\sqrt{\dfrac{75}{3} } }{} +\sqrt[3]{27} } =$

$\dfrac{625-106 }{(\sqrt{3})^{-1} }+\dfrac{36}{\sqrt{25}+3 } }=\\\\\\\dfrac{519.(\sqrt{3})^{3} }{(\sqrt{3})^{-1} .(\sqrt{3})^{3}}+\dfrac{36}{5+3 }=$

$\dfrac{519.\sqrt{3^{2} .3} }{(\sqrt{3})^{2} }+\dfrac{36 }{8}=\\\\\\\dfrac{519.3\sqrt{3} }{3}+\dfrac{18}{4}=\\\\\\519\sqrt{3} +\dfrac{9}{2}=\\\\\\519\sqrt{3} +4,5=$

Bons estudos!!!