Question 15

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 :

Solution

(A): $$\sqrt{3} - \sqrt{2}$$ = $$\dfrac{1}{\sqrt{\ 3}+\sqrt{\ 2}}$$

(B): $$\sqrt{4} - \sqrt{3}$$ = $$\dfrac{1}{\sqrt{\ 4}+\sqrt{\ 3}}$$

(C): $$\sqrt{5} - \sqrt{4}$$ = $$\dfrac{1}{\sqrt{5}+\sqrt{\ 4}}$$

(D): $$\sqrt{2} - 1$$ = $$\dfrac{1}{\sqrt{2}+\sqrt{\ 1}}$$

Now, $$\left(\sqrt{\ 5}+\sqrt{\ 4}\right)>\left(\sqrt{\ 4}+\sqrt{\ 3}\right)>\left(\sqrt{\ 3}+\sqrt{\ 2}\right)>\left(\sqrt{\ 2}+1\right)$$

So, $$\dfrac{1}{\sqrt{\ 5}+\sqrt{\ 4}}<\dfrac{1}{\sqrt{\ 4}+\sqrt{\ 3}}<\dfrac{1}{\sqrt{\ 3}+\sqrt{\ 2}}<\dfrac{1}{\sqrt{\ 2}+1}$$

So, $$D>A>B>C$$

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