What is $\sqrt{192}$ $sqrt192$ in simplest radical form? Thanks!

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What is $\sqrt{192}$ $sqrt192$ in simplest radical form? Thanks!

I need help checking my extra work for practice and wanted to know how to do $\sqrt{192}$ $sqrt192$ as well as the simplest answer in radical form. The answer I got was $8 \sqrt{3}$ $8sqrt3$ if this is not the correct answer, please let me know why. If it is, let me know that I am correct so I don't have to worry about failing my math test in a couple of weeks. Thanks!

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Answer 1 · 2016-10-18T23:31:17

$\sqrt{192} = 8 \sqrt{3}$ $sqrt(192) = 8sqrt(3)$

Explanation:

Your answer is correct. Here's why...

If $a, b \geq 0$ $a, b >= 0$ then:

$\sqrt{a b} = \sqrt{a} \sqrt{b}$ $sqrt(ab) = sqrt(a)sqrt(b)$

If $a \geq 0$ $a >= 0$ then:

$\sqrt{a^{2}} = a$ $sqrt(a^2) = a$

Find the prime factorisation of $192$ $192$ and identify square factors:

$192 = 2 \cdot 2 \cdot 2 \cdot 2 \cdot 2 \cdot 2 \cdot 3 = 2^{6} \cdot 3 = {(2^{3})}^{2} \cdot 3 = 8^{2} \cdot 3$ $192 = 2*2*2*2*2*2*3 = 2^6*3 = (2^3)^2*3 = 8^2*3$

So:

$\sqrt{192} = \sqrt{8^{2} \cdot 3} = \sqrt{8^{2}} \cdot \sqrt{3} = 8 \sqrt{3}$ $sqrt(192) = sqrt(8^2*3) = sqrt(8^2)*sqrt(3) = 8sqrt(3)$

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What is $\sqrt{192}$ $sqrt192$ in simplest radical form? Thanks!

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