Question

Find the Geometric mean between 4/9 and 169/9.

Answer 1

Answer: The geometric mean between 4 and 9 is 6. In general, to find the geometric mean of two numbers, we take the square root, of the product of the two...

Step-by-step explanation:

Answer 2

Geometric mean between two numbers a & b is the square root of the product of two numbers.

Geometric mean of a, b is √ab.

If a, b, c are consecutive terms of Geometric progression, then b is the Geometric mean of a, c because

ac = b² which implies, b = √ac.

Given question,

Geometric mean between 4/9 & 169/9

$= \sqrt{ \frac{4}{9} \times \frac{169}{9} } \\ \\ = \sqrt{ \frac{2 ^{2} \times {13}^{2} }{ {3}^{2} \times {3}^{2} } } \\ \\ = \sqrt{( \frac{2 \times 13}{3 \times 3}) ^{2} } \\ \\ = \frac{2 \times 13}{3 \times 3} \\ \\ = \frac{26}{9}$

Therefore, The Geometric mean of the numbers 4/9 & 169/9 is 26/9.