Arrange the following numbers in increasing order :
A. $$\sqrt{59} - \sqrt{51}$$
B. $$\sqrt{37} - \sqrt{29}$$
C. $$\sqrt{87} - \sqrt{79}$$
D. $$\sqrt{79} - \sqrt{71}$$
Choose the correct answer from the options given below:
8 =Â $$\left(\sqrt{59}-\sqrt{51}\right)\left(\ \sqrt{\ 59}+\sqrt{51}\right)$$
8 =Â $$\left(\sqrt{37}-\sqrt{29}\right)\left(\ \sqrt{37}+\sqrt{29}\right)$$
We know that, $$\sqrt{59}+\sqrt{51}$$ is greater than $$\sqrt{37}+\sqrt{29}$$
This implies, $$\sqrt{37}-\sqrt{29}$$ is greater than $$\sqrt{59}-\sqrt{51}$$ as the product is constant.
Similarly, $$\sqrt{59}-\sqrt{51}$$ is greater than $$\sqrt{79}-\sqrt{71}$$ and $$\sqrt{79}-\sqrt{71}$$ is greater than $$\sqrt{87}-\sqrt{79}$$.
The correct order is B > A > D > C
The answer is option D.
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