Question

The geometric mean of 8 and 50 is​

Answer 1

Given : Numbers 8 and 50

To Find: Geometric mean

Solution:

Two number a , b

arithmetic mean = (a  + b)/2

Geometric mean = √ab

Geometric mean = √ab

a = 8

b = 50

=> Geometric mean = √8 * 50

=> Geometric mean = √2*2*2 * 5*5*2

=> Geometric mean = √2*2*2 * 2 * 5 * 5

=> Geometric mean = 2 * 2 * 5

=> Geometric mean = 20

The geometric mean of 8 and 50 is​  = 20

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Answer 2

Given :- The geometric mean of 8 and 50 is ?

Solution :-

we know that,

• Geometric Mean of a and b is square root of their product .
• GM = √(a * b) .

we have,

• a = 8 .
• b = 50 .

so,

→ GM = √(8 * 50)

→ GM = √{(2 * 2 * 2) * (2 * 5 * 5)}

→ GM = √{(2 * 2) * (2 * 2) * (5 * 5)}

→ GM = √(2² * 2² * 5²)

→ GM = √(2 * 2 * 5)²

→ GM = √(20)²

→ GM = 20 (Ans.)