Mathematics, 18.02.2020 20:32 JasmineFS5181

What is the geometric mean of 6 and 16?

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Answer from: money2tymes

The geometric mean of 6 and 16 is 4√6

Given two integers a and b, the geometric mean of the integers will be expressed as:

GM = √ab

Given the follwing parameteers:

a = 6b = 16

Substitute the given parameters into the formula to have:

GM = √ab

GM = √6(16)

GM = 4√6

Hence the geometric mean of 6 and 16 is 4√6

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Answer from: mia2286

The geometric mean of 6 and 16 = $4\sqrt{6}$

Step-by-step explanation:

The Geometric Mean is basically a special type of average which can be determined

by multiply the numbers together and subsequently taking a square root in case there are two numbers; but we take cube root in case there three numbers etc.

So, lets take the geometric mean of 6 and 16

Considering the number

6 and 16

Step 1: Multiply the numbers i.e. 6 × 16 = 96

Step 2: As there are two number, so just take the square root i.e. $\sqrt{96} =4\sqrt{6}$

In other words:

Geometric Mean of 6 and 16:

$\sqrt{6\times16}$

$=\sqrt{96}$

$\mathrm{Prime\:factorization\:of\:}96:\quad 2^5\cdot \:3$

$=\sqrt{2^5\cdot \:3}$

$=\sqrt{2^4\cdot \:2\cdot \:3}$

$\mathrm{Apply\:radical\:rule}:\quad \sqrt{ab}=\sqrt{a}\sqrt{b},\:\quad \:a\ge 0,\:b\ge 0$

$=\sqrt{2^4}\sqrt{2\cdot \:3}$

$\mathrm{Apply\:radical\:rule}:\quad \sqrt[n]{a^m}=a^{\frac{m}{n}}$

$=2^{\frac{4}{2}}\sqrt{2\cdot \:3}$

$=2^2\sqrt{2\cdot \:3}$

$=4\sqrt{6}$

Therefore, the geometric mean of 6 and 16 = $4\sqrt{6}$

Answer from: Quest

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step-by-step explanation:

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Answer from: Quest

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