Answers to Simplifying Radicals

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Geometric Means Practice

1. Setting up the problem to find the geometric mean between 4 and 16:

First let x be the geometric mean. We know that x divided by 4 equals 16 divided by x or

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2. Solving for the geometric mean:

First we start with our equation from 1, then cross multiply:

The geometric mean between two positive numbers is positive, so we only want the positive solution.

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Generalized Formula for the Geometric Mean

We have two positive numbers a and b such that a < b. We know the geometric mean will be a positive number, x, such that the ratios and will be the same or

cross multiplying gives us:

taking the square roots of both sides (keeping only the positive solution) gives us:

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