Question

Arrange the following in increasing order:
1. 4√3
2. 3√2
3. 6√5
4. 6√7
Choose the correct answer from the options given below:

• A. A < D < B < C
• B. B < C < A < D
• C. A < C < B < D
• D. B < A < C < D

Answer 1

The Correct Option is B

To arrange the given terms in increasing order, we need to compare their magnitudes. The terms provided are:

1. \(4\sqrt{3}\) 
2. \(3\sqrt{2}\)
3. \(6\sqrt{5}\)
4. \(6\sqrt{7}\)

To compare these expressions, calculate the approximate values of each term.

• For \(4\sqrt{3}\): Approximate value is \(4 \times 1.732 = 6.928\)
• For \(3\sqrt{2}\): Approximate value is \(3 \times 1.414 = 4.242\)
• For \(6\sqrt{5}\): Approximate value is \(6 \times 2.236 = 13.416\)
• For \(6\sqrt{7}\): Approximate value is \(6 \times 2.646 = 15.876\)

Arranging these approximated values in increasing order:

• \(3\sqrt{2} = 4.242\)
• \(4\sqrt{3} = 6.928\)
• \(6\sqrt{5} = 13.416\)
• \(6\sqrt{7} = 15.876\)

Hence, the correct order in increasing values is: \(3\sqrt{2} \lt 4\sqrt{3} \lt 6\sqrt{5} \lt 6\sqrt{7}\).

This corresponds to option: B < C < A < D.