Question

2) Usando propriedades, transforme os radicais abaixo em um único radical: d ) 5^1/2. 15^1/2 /3^1/2

Answer 1

$(a*b)^{n}=a^{n}*b^{n}\\(a/b)^{n}=a^{n}/b^{n}$
$\sqrt[n]{a^{x}}=a^{\frac{x}{n}}$
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$5^{\frac{1}{2}}*15^{\frac{1}{2}}/3^{\frac{1}{2}}=(5*15/3)^{\frac{1}{2}}\\5^{\frac{1}{2}}*15^{\frac{1}{2}}/3^{\frac{1}{2}}=(5*5)^{\frac{1}{2}}\\5^{\frac{1}{2}}*15^{\frac{1}{2}}/3^{\frac{1}{2}}=25^{\frac{1}{2}}$
$5^{\frac{1}{2}}*15^{\frac{1}{2}}/3^{\frac{1}{2}}= \sqrt[2]{25^{1}} \\5^{\frac{1}{2}}*15^{\frac{1}{2}}/3^{\frac{1}{2}}= \sqrt{25}\\5^{\frac{1}{2}}*15^{\frac{1}{2}}/3^{\frac{1}{2}}= 5$