Question Video: Finding the Geometric Mean of Two Numbers Mathematics • Second Year of Secondary School

Video Transcript

Find the geometric mean of 16 and four.

Remember, if two numbers 𝑎 and 𝑏 have the same sign, then their geometric mean is the square root of 𝑎 times 𝑏. Our two numbers are 16 and four, and they’re both positive. So, let’s let 𝑎 be equal to 16 and 𝑏 be equal to four. Their geometric mean then is the square root of 16 times four. And whilst we can apply the laws of radicals to simplify this, in fact 16 times four is 64, which is itself a square number. So, since the square root of 64 is equal to eight, the geometric mean of 16 and four is eight.