1- USE A PROPRIEDADE DO PRODUTO DAS RAÍZES E DETERMINE O VALOR DE:A)1- USE A PROPRIEDADE DO PRODUTO DAS RAÍZES E DETERMINE O VALOR DE:
A) √49 · √¨¨36¨¨.¨ 25¨¨ ;
B)√¨¨13²¨¨.25¨¨
C) ⁵√3² . ⁵√3³;
D)∛5⁶;
E)³√8¨¨.64 .√49;
F) 2. √2. √18 ;
Soluções para a tarefa
Respondido por
47
a)
b)
![\sqrt{13^{2}}*\sqrt{25}=\sqrt[2]{13^{2}}*5\\\sqrt{13^{2}}*\sqrt{25}=13^{\frac{2}{2}}*5\\\sqrt{13^{2}}*\sqrt{25}=13^{1}*5\\\sqrt{13^{2}}*\sqrt{25}=13*5\\\sqrt{13^{2}}*\sqrt{25}=65](https://tex.z-dn.net/?f=%5Csqrt%7B13%5E%7B2%7D%7D%2A%5Csqrt%7B25%7D%3D%5Csqrt%5B2%5D%7B13%5E%7B2%7D%7D%2A5%5C%5C%5Csqrt%7B13%5E%7B2%7D%7D%2A%5Csqrt%7B25%7D%3D13%5E%7B%5Cfrac%7B2%7D%7B2%7D%7D%2A5%5C%5C%5Csqrt%7B13%5E%7B2%7D%7D%2A%5Csqrt%7B25%7D%3D13%5E%7B1%7D%2A5%5C%5C%5Csqrt%7B13%5E%7B2%7D%7D%2A%5Csqrt%7B25%7D%3D13%2A5%5C%5C%5Csqrt%7B13%5E%7B2%7D%7D%2A%5Csqrt%7B25%7D%3D65 "\sqrt{13^{2}}*\sqrt{25}=\sqrt[2]{13^{2}}*5\\\sqrt{13^{2}}*\sqrt{25}=13^{\frac{2}{2}}*5\\\sqrt{13^{2}}*\sqrt{25}=13^{1}*5\\\sqrt{13^{2}}*\sqrt{25}=13*5\\\sqrt{13^{2}}*\sqrt{25}=65")
* Ou seja:![\sqrt[n]{a^{n}}=a](https://tex.z-dn.net/?f=+%5Csqrt%5Bn%5D%7Ba%5E%7Bn%7D%7D%3Da+ "\sqrt[n]{a^{n}}=a")
c)
![\sqrt[5]{3^{2}} *\sqrt[5]{3^{3}}=\sqrt[5]{3^{2}*3^{3}}\\\sqrt[5]{3^{2}} *\sqrt[5]{3^{3}}=\sqrt[5]{3^{5}}\\\sqrt[5]{3^{2}} *\sqrt[5]{3^{3}}=3](https://tex.z-dn.net/?f=%5Csqrt%5B5%5D%7B3%5E%7B2%7D%7D+%2A%5Csqrt%5B5%5D%7B3%5E%7B3%7D%7D%3D%5Csqrt%5B5%5D%7B3%5E%7B2%7D%2A3%5E%7B3%7D%7D%5C%5C%5Csqrt%5B5%5D%7B3%5E%7B2%7D%7D+%2A%5Csqrt%5B5%5D%7B3%5E%7B3%7D%7D%3D%5Csqrt%5B5%5D%7B3%5E%7B5%7D%7D%5C%5C%5Csqrt%5B5%5D%7B3%5E%7B2%7D%7D+%2A%5Csqrt%5B5%5D%7B3%5E%7B3%7D%7D%3D3 "\sqrt[5]{3^{2}} *\sqrt[5]{3^{3}}=\sqrt[5]{3^{2}*3^{3}}\\\sqrt[5]{3^{2}} *\sqrt[5]{3^{3}}=\sqrt[5]{3^{5}}\\\sqrt[5]{3^{2}} *\sqrt[5]{3^{3}}=3")
d)
![\sqrt[3]{5^{6}}=5^{\frac{6}{3}}\\\sqrt[3]{5^{6}}=5^{2}\\\sqrt[3]{5^{6}}=25](https://tex.z-dn.net/?f=%5Csqrt%5B3%5D%7B5%5E%7B6%7D%7D%3D5%5E%7B%5Cfrac%7B6%7D%7B3%7D%7D%5C%5C%5Csqrt%5B3%5D%7B5%5E%7B6%7D%7D%3D5%5E%7B2%7D%5C%5C%5Csqrt%5B3%5D%7B5%5E%7B6%7D%7D%3D25 "\sqrt[3]{5^{6}}=5^{\frac{6}{3}}\\\sqrt[3]{5^{6}}=5^{2}\\\sqrt[3]{5^{6}}=25")
e)
![\sqrt[3]{8}*\sqrt{64}*\sqrt{49}=\sqrt[3]{2^{3}}*8*7\\\sqrt[3]{8}*\sqrt{64}*\sqrt{49}=2*8*7\\\sqrt[3]{8}*\sqrt{64}*\sqrt{49}=112](https://tex.z-dn.net/?f=%5Csqrt%5B3%5D%7B8%7D%2A%5Csqrt%7B64%7D%2A%5Csqrt%7B49%7D%3D%5Csqrt%5B3%5D%7B2%5E%7B3%7D%7D%2A8%2A7%5C%5C%5Csqrt%5B3%5D%7B8%7D%2A%5Csqrt%7B64%7D%2A%5Csqrt%7B49%7D%3D2%2A8%2A7%5C%5C%5Csqrt%5B3%5D%7B8%7D%2A%5Csqrt%7B64%7D%2A%5Csqrt%7B49%7D%3D112 "\sqrt[3]{8}*\sqrt{64}*\sqrt{49}=\sqrt[3]{2^{3}}*8*7\\\sqrt[3]{8}*\sqrt{64}*\sqrt{49}=2*8*7\\\sqrt[3]{8}*\sqrt{64}*\sqrt{49}=112")
f)
b)
* Ou seja:
c)
d)
e)
f)
Perguntas interessantes