Question

Classify the given pair of surds into like surds and unlike surds.

(i) $\sqrt{52},5\sqrt{13}$ (ii) $\sqrt{68},5\sqrt{3}$ (iii) $4\sqrt{18},7\sqrt{2}$ (iv) $19\sqrt{12},6\sqrt{3}$ (v) $5\sqrt{22},7\sqrt{33}$ (vi) $5\sqrt{5},\sqrt{75}$

Answer 1

(i) $\sqrt{52},5\sqrt{13}$

Since, $\sqrt{52}=\sqrt{4\times 13}=2\sqrt{13}$

So, $\sqrt{52},5\sqrt{13}$ is like surds.

(ii) $\sqrt{68},5\sqrt{3}$

Since, $\sqrt{68}=\sqrt{4\times 17}=2\sqrt{17}$

So, $\sqrt{68},5\sqrt{3}$ is unlike surds.

(iii) $4\sqrt{18},7\sqrt{2}$

Since, $4\sqrt{18}=4\sqrt{9\times 2}=4\times 3\sqrt{2}=12\sqrt{2}$

So, $4\sqrt{18},7\sqrt{2}$ is like surds.

(iv) $19\sqrt{12},6\sqrt{3}$

Since, $19\sqrt{12}=19\sqrt{4\times 3}=19\times 2\sqrt{3}=38\sqrt{3}$

So, $19\sqrt{12},6\sqrt{3}$ is like surds.

(v) $5\sqrt{22},7\sqrt{33}$

Since, $5\sqrt{22}=5\sqrt{2\times 11}\mathrm{and}7\sqrt{33}=7\sqrt{3\times 11}$

So, $5\sqrt{22},7\sqrt{33}$ is unlike surds.

(vi) $5\sqrt{5},\sqrt{75}$

Since, $\sqrt{75}=\sqrt{25\times 3}=5\sqrt{3}$

So, $5\sqrt{5},\sqrt{75}$ is like surds.