Question

The rationalising factor of $\sqrt[7]{7x^3{y}^5{z}^2}$ is _________.

• A. $\sqrt[7]{7z^5{y}^2{x}^4}$
• B. $\sqrt[4]{4x^3{y}^{2}z}$
• C. $\sqrt{x^4{y}^2{z}^5}$
• D. $\sqrt[3]{3y^2{x}^4{z}^3}$

Answer 1

Answer: (A)

$\sqrt[7]{7z^5{y}^2{x}^4}$

Given number : $\sqrt[7]{7x^3{y}^5{z}^2}=x^{\frac{3}{7}}{y}^{\frac{5}{7}}{z}^{\frac{2}{7}}$

Rationalising factor is the number which when multiplied with given number removes all surds.

$\therefore$ Rationalising factor $=x^{1-\frac{3}{7}}{y}^{1-\frac{5}{7}}{z}^{1-\frac{2}{7}}=\sqrt[7]{7x^4{y}^2{z}^5}$