Question

Se √13²-12² = raiz n de 125, então o valor de "n" é?

Answer 1

$\sqrt{13^{2}-12^{2}}=\sqrt[n]{125}\\\\\sqrt{169-144}=125^{\frac{1}{n}}\\\\\sqrt{25}=125^{\frac{1}{n}}\\\\5=125^{\frac{1}{n}}\\\\5=(5^{3})^{\frac{1}{n}}\\\\5=5^{3.(\frac{1}{n})}\\\\5=5^{\frac{3}{n}}\\\\1=\frac{3}{n}\\\\n.1=3\\\\n=3$