Sobre Radiciação
editar
- Coloque em ordem crescente:
![{\displaystyle {\sqrt[{3}]{11}},{\sqrt {5}},2{\sqrt {2}}\,}](https://wikimedia.org/api/rest_v1/media/math/render/svg/9208c53ed4f10692dd82202b6b4519d43ddc211d)
- Expresse sob a forma de raiz as expressões abaixo:
![{\displaystyle {\sqrt[{3}]{{\frac {x}{y}}{\sqrt[{4}]{\frac {x^{2}}{y}}}}}\,}](https://wikimedia.org/api/rest_v1/media/math/render/svg/cc9ec5f02fb85076774695d085d2a115c4563cb4)
![{\displaystyle {\sqrt[{4}]{\frac {36}{125}}}{\sqrt[{3}]{\frac {5}{4}}}\,}](https://wikimedia.org/api/rest_v1/media/math/render/svg/1d160b650dacb1f926ab2c3a6521643287a3f390)
![{\displaystyle {\sqrt[{6}]{x^{2}y}}{\sqrt[{4}]{x^{3}y^{2}}}\,}](https://wikimedia.org/api/rest_v1/media/math/render/svg/0b34bc1ff07f6a9b7d3d1e34df07cf8c51efb3f7)
- Os lados de um triângulo valem
cm, 
cm e 
cm. Calcule seu perímetro.
- Simplifique os radicais
![{\displaystyle {\sqrt[{3}]{\frac {4^{2}}{9^{4}}}}\,}](https://wikimedia.org/api/rest_v1/media/math/render/svg/d547c528583c3c205f760109cb01cc5aa4fc37f7)
![{\displaystyle {\sqrt[{4}]{\frac {x^{6}.y^{9}}{z^{7}}}}\,}](https://wikimedia.org/api/rest_v1/media/math/render/svg/f1749950535738833be91ee2b98dd4266a48beb0)
- Racionalize as expressões abaixo:
![{\displaystyle {\frac {\sqrt[{5}]{8}}{\sqrt[{5}]{4}}}=\,}](https://wikimedia.org/api/rest_v1/media/math/render/svg/c42f36a462afc4fd63e0cb340046e6dd6159c8ad)
![{\displaystyle {\frac {100}{{\sqrt[{3}]{2}}{\sqrt[{4}]{5}}}}=\,}](https://wikimedia.org/api/rest_v1/media/math/render/svg/56b10096a5884b1e5d3e2c2d85d7b1f6d1fc9c21)
![{\displaystyle {\frac {{\sqrt[{3}]{4}}+{\sqrt[{3}]{9}}}{{\sqrt[{3}]{2}}+{\sqrt[{3}]{3}}}}=\,}](https://wikimedia.org/api/rest_v1/media/math/render/svg/d4fe019ce04a9413a01e7165d282b3a7db9b9c91)
- Transforme as expressões em um único radical:
![{\displaystyle {\sqrt[{3}]{x{\sqrt[{3}]{x{\sqrt[{3}]{x}}}}}}=\,}](https://wikimedia.org/api/rest_v1/media/math/render/svg/c69d07d7ac3e57f566de4ee699bf270915adabf2)
![{\displaystyle {\sqrt[{4}]{x^{3}{\sqrt[{3}]{x^{2}{\sqrt {x}}}}}}=\,}](https://wikimedia.org/api/rest_v1/media/math/render/svg/f0fd4fc5ed763429e83e6a78bb4ce17da3936ca5)
![{\displaystyle {\sqrt[{10}]{x^{3}}}{\sqrt[{6}]{x^{5}}}=\,}](https://wikimedia.org/api/rest_v1/media/math/render/svg/967eb0881cfef8b57ce3e1618b4565f2608ed638)
![{\displaystyle {\frac {\sqrt[{5}]{8}}{\sqrt[{3}]{4}}}=\,}](https://wikimedia.org/api/rest_v1/media/math/render/svg/556eb96fb411c4183a446dbdafebf441c486a5db)
![{\displaystyle {\frac {125}{{\sqrt {5}}{\sqrt[{3}]{25}}}}=\,}](https://wikimedia.org/api/rest_v1/media/math/render/svg/e6c775f274c01f62da5a285c0a78750c7582ca7e)
- Coloque a expressão na forma mais simples, conforme o exemplo do exercício 1:
![{\displaystyle {\sqrt[{3}]{\frac {x^{4}\ y^{2}}{2\ z}}}\,}](https://wikimedia.org/api/rest_v1/media/math/render/svg/c68f5d8d8a513f46826eecac85c422cef8f98484)
= ![{\displaystyle {\sqrt[{3}]{\frac {x^{3}\ x\ y^{2}\ 2^{2}\ z^{2}}{2^{3}\ z^{3}}}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/71175ca1068e18d758b1353adf8ae11647869915)
= ![{\displaystyle {\sqrt[{3}]{\frac {x^{3}}{2^{3}\ z^{3}}}}{\sqrt[{3}]{x\ 2^{2}\ y^{2}\ z^{2}}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/0fb2763d944fdccd180d19887941ac4face45c23)
= ![{\displaystyle {\frac {x}{2\ z}}{\sqrt[{3}]{2^{2}\ x\ y^{2}\ z^{2}}}\,}](https://wikimedia.org/api/rest_v1/media/math/render/svg/fe90479f96a7bf9b8305d79dcada2edc33c212e3)
![{\displaystyle {\sqrt[{5}]{\frac {64}{81}}}=\,}](https://wikimedia.org/api/rest_v1/media/math/render/svg/0568519a42f821120758206e6a00cc09276e8b1c)
![{\displaystyle {\sqrt[{15}]{x^{32}\ y^{83}\ z^{41}}}=\,}](https://wikimedia.org/api/rest_v1/media/math/render/svg/e9fa9333fa949ab0f49643889eea3938affb8e75)
- Escreva as expressões abaixo como uma soma de radicais:
- Seja x um número real positivo tal que
é o inverso de 
. Determine 
.
- Seja
e 
. Determine a:b.
- Simplifique as expressões abaixo:
![{\displaystyle {\frac {1}{\sqrt[{3}]{2}}}+{\frac {1}{\sqrt[{3}]{4}}}-{\frac {1}{\sqrt[{3}]{16}}}=\,}](https://wikimedia.org/api/rest_v1/media/math/render/svg/3f181c890a93a10f98b21a6389238678b75a0770)
![{\displaystyle ({\sqrt[{3}]{9}}-{\sqrt[{3}]{3}})^{2}=\,}](https://wikimedia.org/api/rest_v1/media/math/render/svg/f36d173457426711eafed96bfc2908e855ca550b)
== Veja também ==Leonardo Belo Nato
