# How do you simplify #sqrt(108x^6y^4z^5)#?

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To simplify √(108x^6y^4z^5), you can break down 108 into its prime factors, and then apply the properties of radicals to simplify the expression.

First, factor 108:

108 = 2^2 * 3^3

Then, rewrite the expression using the prime factorization:

√(108x^6y^4z^5) = √((2^2 * 3^3) * x^6 * y^4 * z^5)

Now, apply the property of radicals that allows you to separate the radicals of individual factors:

√(108x^6y^4z^5) = √(2^2) * √(3^3) * √(x^6) * √(y^4) * √(z^5)

Next, simplify each radical:

√(2^2) = 2 √(3^3) = 3√3 √(x^6) = x^3 √(y^4) = y^2 √(z^5) = z^(5/2)

Now, put these simplified radicals back together:

2 * 3√3 * x^3 * y^2 * z^(5/2)

So, the simplified form of √(108x^6y^4z^5) is 2x^3y^2z^(5/2)√3.

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