Question

Arrange the following surds in increasing order.

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

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

Answer 1

The Correct Option is D

We calculate the approximate numerical values of the surds:

\[ A = \sqrt[3]{2} \approx 1.26, \quad B = \sqrt{3} \approx 1.73, \quad C = \sqrt[4]{5} \approx 1.50, \quad D = \sqrt[6]{7} \approx 1.40 \]

Now, arranging the surds in increasing order:

\[ A \approx 1.26, \quad D \approx 1.40, \quad C \approx 1.50, \quad B \approx 1.73 \]

Thus, the increasing order is:

\[A < D < C < B\]