Question

Which pair of numbers are rationalising factors to one another.

• A. $2\sqrt{3}$ and $\sqrt{3}$
• B. $3^{\frac{1}{3}}-3^{\frac{-1}{3}}$ and $3^{\frac{2}{3}}+1+3^{\frac{-2}{3}}$
• C. $x^{\frac{1}{x}}-x^{\frac{-1}{n}}$ and$(x^{\frac{n-1}{n}}-x^{\frac{n-2}{n}}+.....x^{-\left(\frac{n-1}{n}\right)})$
• D. $\sqrt[3]{35}+\frac{1}{\sqrt[3]{35}}$ and $\sqrt[3]{35^2}+1-\frac{1}{\sqrt[3]{35^2}}$

Answer 1

Answer: (A), (B)

The correct options are
A $2\sqrt{3}$ and $\sqrt{3}$
B $3^{\frac{1}{3}}-3^{\frac{-1}{3}}$ and $3^{\frac{2}{3}}+1+3^{\frac{-2}{3}}$

(A, B) $2\sqrt{3}\times \sqrt{3}=2\times 3=6$$\left (3^{\frac{1}{3}}-3^{\frac{-1}{3}} \right )\left (3^{\frac{2}{3}}+1+3^{\frac{-2}{3}}
\right )$
$=3-\frac{1}{3}=\frac{8}{3}$