Question

me ajudem rápido pfvr dou 5 estrelas e 20 pontos​

Answer 1

Resposta:

a) $\sqrt{11}$

b) $\sqrt{\left(\frac{2}{7}\right)}$

c) $3\sqrt[8]{729}$

d) $5\sqrt[15]{9765625}$

e) $\sqrt[5]{2}$

f) $3$

g) $\sqrt[3]{3.1}$

h) $\sqrt[3]{9}$

i) $2$

j) $\frac{1}{2}$

Explicação passo a passo:

Para resolvermos esse tipo de questão, precisamos aplicar as propriedades dos radicais:

$\sqrt[n]{a} =a^{\frac{1}{n} }$

Além disso, vamos usar também as propriedades dos expoentes:

$(a^{b} )^c=a^b^c$

Simplificando os radicais de fato:

$A)\\\\\sqrt[4]{11^2}\\\\\left(11^2\right)^{\frac{1}{4}}\\\\11^{2\cdot \frac{1}{4}}\\\\11^{\frac{1}{2}}\\\\\sqrt{11}$

$B)\\\left(\sqrt[8]{\left(\frac{2}{7}\right)}\right)^4\\\\\left(\left(\left(\frac{2}{7}\right)\right)^{\frac{1}{8}}\right)^4\\\\\left(\left(\frac{2}{7}\right)\right)^{\frac{1}{8}\cdot \:4}\\\\\left(\left(\frac{2}{7}\right)\right)^{\frac{1}{2}}\\\\\sqrt{\left(\frac{2}{7}\right)}$

$C)\\\\\sqrt[8]{3^{14}}\\\\\sqrt[8]{3^8\cdot \:3^6}\\\\\sqrt[8]{3^8}\sqrt[8]{3^6}\\\\3\sqrt[8]{3^6}\\\\3\sqrt[8]{729}$

$D)\\\\\sqrt[15]{5^{25}}\\\\\sqrt[15]{5^{15}\cdot \:5^{10}}\\\\\sqrt[15]{5^{15}}\sqrt[15]{5^{10}}\\\\5\sqrt[15]{5^{10}}\\\\5\sqrt[15]{9765625}$

$E)\\\\\sqrt[10]{2^2}\\\\\left(2^2\right)^{\frac{1}{10}}\\\\2^{2\cdot \frac{1}{10}}\\\\2^{\frac{1}{5}}\\\\\sqrt[5]{2}$

$F)\\\\\sqrt[4]{81}\\\\81=3^4\\\\\sqrt[4]{3^4}\\\\\sqrt[4]{3^4}=3$

$G)\\\\\sqrt[15]{3.1^5}\\\\\left(3.1^5\right)^{\frac{1}{15}}\\\\3.1^{5\cdot \frac{1}{15}}\\\\3.1^{\frac{1}{3}}\\\\\sqrt[3]{3.1}$

$H)\\\\\sqrt[12]{9^4}\\\\\left(9^4\right)^{\frac{1}{12}}\\\\9^{4\cdot \frac{1}{12}}\\\\9^{\frac{1}{3}}\\\\\sqrt[3]{9}$

$i)\\\\\sqrt[4]{16}\\\\16=2^4\\\\\sqrt[4]{2^4}\\\\2$

$J)\\\\\sqrt[6]{\frac{1}{64}}\\\\\frac{\sqrt[6]{1}}{\sqrt[6]{64}}\\\\\frac{1}{\sqrt[6]{64}}\\\\\frac{1}{2}$

Aprenda mais sobre simplificação de radicais aqui: https://brainly.com.br/tarefa/20451178