Question

Arrange the following in descending order. (A) $\sqrt{3} - \sqrt{2}$ (B) $\sqrt{4} - \sqrt{3}$ (C) $\sqrt{5} - \sqrt{4}$ (D) $\sqrt{2} - 1$ Choose the correct answer from the options given below :

Accepted Answer

C. Rationalize each expression: - (A) $\sqrt{3}-\sqrt{2} = \frac{1}{\sqrt{3}+\sqrt{2}}$ - (B) $\sqrt{4}-\sqrt{3} = \frac{1}{\sqrt{4}+\sqrt{3}}$ - (C) $\sqrt{5}-\sqrt{4} = \frac{1}{\sqrt{5}+\sqrt{4}}$ - (D) $\sqrt{2}-1 = \frac{1}{\sqrt{2}+1}$ Since denominators follow: $\sqrt{2}+1 < \sqrt{3}+\sqrt{2} < \sqrt{4}+\sqrt{3} < \sqrt{5}+\sqrt{4}$, Inverting gives: $D > A > B > C$.

Descending Order of Square Root Differences

Explanation

Practise this under exam conditions