SOLUTION: What is the geometric mean of 7 and 56? Came up with 18sqrt68 but that answer is wrong for some reason.

Question 318341: What is the geometric mean of 7 and 56?
Came up with 18sqrt68 but that answer is wrong for some reason.
Answer by solver91311(24713) (Show Source): You can put this solution on YOUR website!

Take the square root of the product.

Took me a few minutes, but I figured out what you did. You said that 324 is a perfect square, namely 18 squared, so you subtracted 324 from 392 leaving 68. If this were the TV show NCIS, EVERYONE in the cast would slap the back of your head for that one.

The process of simplifying the radicand in a square root is as follows:

Perform the prime factorization of the radicand. For every pair of equal factors, eliminate them under the radical and take one out of the radical. Leave all single prime factors under the radical.

To recap, the prime factorization of 392 is three factors of 2 and two factors of 7.

Eliminate two of the 2s. One 2 goes outside. Eliminate both of the 7s. One 7 goes outside. The result is a 2 and a 7 outside for 14 and a 2 inside.

John

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