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Kathryn Kingham

Find the geometric mean of (π β 19) and (π + 19).

Find the geometric mean of π minus 19 and π plus 19.

The geometric mean of two values π and π is the square root of π times π, which means we need to multiply π minus 19 times π 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. π times π equals π squared. π times 19 equals 19π. Negative 19 times π equals negative 19π. And negative 19 times 19 equals negative 361.

This middle term says 19π minus 19π and that equals zero. They cancel each other out. We now have π squared minus 361. And we must take the square root of that value.

And our geometric mean is then the square root of π squared minus 361.

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