Question

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:

• A. \(B < A < D < C\)
• B. \(C < D < B < A\)
• C. \(B < A < C < D\)
• D. \(C < D < A < B\)

Answer 1

The Correct Option is D

To solve the problem of arranging the numbers in increasing order, we need to compare each expression given in the problem: 

1. Expression A: \(\sqrt{59} - \sqrt{51}\)
2. Expression B: \(\sqrt{37} - \sqrt{29}\)
3. Expression C: \(\sqrt{87} - \sqrt{79}\)
4. Expression D: \(\sqrt{79} - \sqrt{71}\)

We will approximate the square roots of the numbers to compare these expressions:

• \(\sqrt{59} \approx 7.68\)
• \(\sqrt{51} \approx 7.14\)
• \(\sqrt{37} \approx 6.08\)
• \(\sqrt{29} \approx 5.38\)
• \(\sqrt{87} \approx 9.33\)
• \(\sqrt{79} \approx 8.89\)
• \(\sqrt{71} \approx 8.43\)

Now let's calculate the differences:

• Difference A: \(\sqrt{59} - \sqrt{51} \approx 7.68 - 7.14 = 0.54\)
• Difference B: \(\sqrt{37} - \sqrt{29} \approx 6.08 - 5.38 = 0.70\)
• Difference C: \(\sqrt{87} - \sqrt{79} \approx 9.33 - 8.89 = 0.44\)
• Difference D: \(\sqrt{79} - \sqrt{71} \approx 8.89 - 8.43 = 0.46\)

Therefore, the order of the differences from smallest to largest is:

• \(C: 0.44\)
• \(D: 0.46\)
• \(A: 0.54\)
• \(B: 0.70\)

Thus, the correct order is \(C < D < A < B\), which corresponds to the answer: \(C < D < A < B\).