Question

Two irrational numbers \[\sqrt6\] and \[\sqrt5\].

Statement (1): The mean proportion of \[\sqrt6\] and \[\sqrt5\] is \[\frac{\sqrt6 +\sqrt5}2\].

Statement (2): The mean proportion of two positive real numbers 𝑥 and 𝑦 is \[\sqrt{𝑥×𝑦}\].

Options

• Both the statements are true.

• Both the statements are false.

• Statement 1 is true, and statement 2 is false.

• Statement 1 is false, and statement 2 is true.

Answer 1

Statement 1 is false, and statement 2 is true.

Explanation:

The mean proportion of two positive real numbers x and y is \[\sqrt {x × y}\]

The mean proportion of \[\sqrt{6} \text{ and } \sqrt{5} = \sqrt{\sqrt{6} \times \sqrt{5}} \]

\[ = \sqrt{\sqrt{30}} = \sqrt[4]{30} \]

So, statement 1 is false but statement 2 is true.