Find the geometric mean of 𝑎 minus 19 and 𝑎 plus 19.
The geometric mean of two values 𝑎 and 𝑏 is the square root of 𝑎 times 𝑏, which means we need to multiply 𝑎 minus 19 times 𝑎 plus 19 and then take the square root of that value.
Our first step will start by multiplying. We need to FOIL these two expressions. 𝑎 times 𝑎 equals 𝑎 squared. 𝑎 times 19 equals 19𝑎. Negative 19 times 𝑎 equals negative 19𝑎. And negative 19 times 19 equals negative 361.
This middle term says 19𝑎 minus 19𝑎 and that equals zero. They cancel each other out. We now have 𝑎 squared minus 361. And we must take the square root of that value.
And our geometric mean is then the square root of 𝑎 squared minus 361.