Question

Write the order of the following surds:

(i) $\sqrt{50}$

(ii) $\sqrt[3]{5}$

(iii) $\sqrt{{31}^{\frac{1}{3}}}$

(iv) ${}^3\sqrt{(9{)}^2}$

(v) $\sqrt[4]{\frac{31}{50}}$

Answer 1

Surd $\sqrt[n]{a}$ is said to be of the order 'n'.

(i) The order of $\sqrt{50}$ is 2.

(ii) The order of $\sqrt[3]{5}$ is 3.

(iii) The order of $\sqrt[]{{31}^{\frac{1}{3}}}\left(\mathrm{i}.\mathrm{e}.\sqrt[6]{31}\right)$ is 6.

(iv) The order of $\sqrt[3]{9^2}\left(\mathrm{i}.\mathrm{e}.\sqrt[3]{81}\right)$ is 3.

(v) The order of $\sqrt[4]{\frac{31}{50}}$ is 4.