Question

The mean proportional between $8 + 4\sqrt 2 and 6-3\sqrt 2$

• A. $$\sqrt{6}$$
• B. $$3\sqrt{6}$$
• C. $$2\sqrt{6}$$
• D. $$4\sqrt{6}$$

Answer 1

Answer:

$$2\sqrt{6}$$

Solution: Given: Two terms 8 + 4√2 and 6 - 3√2 Explanation: The square root of the product of two numbers(a & b) when expressed as the means of a proportion. For example: a/x : x/b Calculation: Let 'x' be the mean proportional value. (8 + 4√2)/x : x/(6 - 3√2) ⇒ x2 = (8 + 4√2) × (6 - 3√2) ⇒ x2 = 48 - 24√2 + 24√2 - 24 ⇒ x2 = 24 ⇒ x = 2√6 ∴ The mean proportional value is 2√6