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Simplify.
Remove all perfect squares from inside the square roots. Assume
x and
z are positive.

sqrt(72x^(3)z^(3))=

Simplify. $\newline$ Remove all perfect squares from inside the square roots. Assume $\newline$ $x$ and $\newline$ $z$ are positive. $\newline$ $\sqrt{72x^{3}z^{3}}$ =

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Simplify radical expressions with variables

Full solution

Q. Simplify.

\newline

Remove all perfect squares from inside the square roots. Assume

\newline

x

and

\newline

z

are positive.

\newline

\sqrt{72x^{3}z^{3}}

=

Factorize the expression: Factorize the expression inside the square root to identify perfect squares. $\newline$ We need to factorize $72x^3z^3$ to find perfect squares. The prime factorization of $72$ is $2^3 \times 3^2$ . So, we can write $72x^3z^3$ as $(2^3 \times 3^2 \times x^3 \times z^3)$ .
Group the factors into perfect squares: Group the factors into perfect squares. $\newline$ We can group the factors as follows: $(2^2 \cdot 2) \cdot (3^2) \cdot (x^2 \cdot x) \cdot (z^2 \cdot z)$ . Here, $2^2$ , $3^2$ , $x^2$ , and $z^2$ are perfect squares.
Take the square root of the expression: Take the square root of the expression, separating the perfect squares from the non-perfect squares. $\newline$ The square root of the expression becomes $\sqrt{2^2 \cdot 3^2 \cdot x^2 \cdot z^2} \cdot \sqrt{2 \cdot x \cdot z}$ .
Simplify the square root of the perfect squares: Simplify the square root of the perfect squares and leave the rest inside the square root. $\newline$ Since the square root of a perfect square is just the base of the square, we get $2 \times 3 \times x \times z \times \sqrt{2 \times x \times z}$ .
Combine the coefficients and simplify the expression: Combine the coefficients and simplify the expression. $\newline$ The final simplified expression is $6xz \times \sqrt{2xz}$ .

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