Nagwa uses cookies to ensure you get the best experience on our website. Learn more about our Privacy Policy.

Video: Finding the Geometric Mean of Two Expressions

Kathryn Kingham

Find the geometric mean of (π‘Ž βˆ’ 19) and (π‘Ž + 19).

01:19

Video Transcript

Find the geometric mean of π‘Ž minus 19 and π‘Ž plus 19.

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

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

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