Rationalizing Factor of 3√9A) \(\sqrt[3]{3}\)B) \(\sqrt[3]{6}\)C)

1.	Rationalizing Factor of 3√9A) \(\sqrt[3]{3}\)B) \(\sqrt[3]{6}\)C) \(\sqrt[3]{9}\)D) \(\sqrt[3]{27}\)
Answer» Correct option is (A) \(\sqrt[3]{3}\) \(\sqrt[3]{9}=(9)^\frac13=(3^2)^\frac13=(3)^\frac23\) \(\because\) \((3)^\frac23\times(3)^\frac13=3^{(\frac23+\frac13)}\) \(=3^1=3\) which is a rational number. i.e., \(\sqrt[3]{9}\times\sqrt[3]{3}=3\) a rational number. It implies \(\sqrt[3]{3}\) is a rationalising factor of \(\sqrt[3]{9}.\) Correct option is A) \(\sqrt[3]{3}\)

Rationalizing Factor of 3√9A) \(\sqrt[3]{3}\)B) \(\sqrt[3]{6}\)C) \(\sqrt[3]{9}\)D) \(\sqrt[3]{27}\)

Answer»

Correct option is (A) \(\sqrt[3]{3}\)

\(\sqrt[3]{9}=(9)^\frac13=(3^2)^\frac13=(3)^\frac23\)

\(\because\) \((3)^\frac23\times(3)^\frac13=3^{(\frac23+\frac13)}\) \(=3^1=3\) which is a rational number.

i.e., \(\sqrt[3]{9}\times\sqrt[3]{3}=3\) a rational number.

It implies \(\sqrt[3]{3}\) is a rationalising factor of \(\sqrt[3]{9}.\)

Correct option is A) \(\sqrt[3]{3}\)