Question

Qual a raiz quadrada se 529 elevado ao 9?

Answer 1

Resposta:

Qual a raiz quadrada se 529 elevado ao 9?

$\sqrt{529^{9}$

$529^{8+1}=529^8\cdot \:529$

$=\sqrt{529^8\cdot \:529}$

$\sqrt{529^8\cdot \:529}=\sqrt{529^8}\sqrt{529}$

$=\sqrt{529^8}\sqrt{529}$

$=529^4\sqrt{529}$

Aplicar as leis dos expoentes:$\sqrt{a}=a^{\frac{1}{2}}$

$\sqrt{529}=529^{\frac{1}{2}}$

$=529^4\cdot \:529^{\frac{1}{2}}$

$529^4\cdot \:529^{\frac{1}{2}}=529^{4+\frac{1}{2}}$

$=529^{4+\frac{1}{2}}$

$=529^{\frac{9}{2}}$

Descompor o número em factores primos: 529=23²

$=\left(23^2\right)^{\frac{9}{2}}$

$\left(23^2\right)^{\frac{9}{2}}=23^{2\cdot \frac{9}{2}}$

$=23^{2\cdot \frac{9}{2}}$

$=23^9$ = decimais:1,801152661463

Explicação passo-a-passo:

espero ter ajudado