if a is the g.m. of 2 and 1/4, then find a.
Assuming g.m. stands for geometric mean
the terms are 2, a, and 1/4
and
a/2 = (1/4)/a
a^2 = 1/2
a = ± 1/√2 or ± √2/2
To find the geometric mean (g.m.) of a number, we need to understand what the geometric mean is. The geometric mean is the square root of the product of two or more numbers.
In this case, we are given that the geometric mean (a) is equal to 2 and 1/4. To find the value of a, we need to express 2 and 1/4 as a decimal or fraction.
To do that, we can convert the mixed number 2 and 1/4 to an improper fraction:
2 and 1/4 = (2 * 4 + 1) / 4 = 9 / 4
Now that we have expressed 2 and 1/4 as the fraction 9/4, we can find the value of a by taking the square root of 9/4:
a = √(9/4)
To simplify the square root, we can simplify the fraction inside the square root:
a = √(9/4) = √9 / √4 = 3/2
Therefore, the value of a is 3/2 or 1.5.