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Simplify. Assume $q$ is greater than or equal to zero. $\newline$ $\sqrt{18q^4}$

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Simplify radical expressions with variables

Full solution

Q. Simplify. Assume

q

is greater than or equal to zero.

\newline

\sqrt{18q^4}

Factorize $18q^4$ : Factorize $18q^4$ to find perfect squares. $\newline$ The complete factorization of $18q^4$ is $2 \times 3 \times 3 \times q^2 \times q^2$ .
Group perfect squares: Group the factors into perfect squares inside the radical. $\sqrt{18q^4}$ becomes $\sqrt{2 \times 3^2 \times q^2 \times q^2}$ .
Simplify square roots: Simplify the square root of the perfect squares. $\sqrt{2 \times 3^2 \times q^2 \times q^2}$ simplifies to $3 \times q \times q \times \sqrt{2}$ because the square root of $3^2$ is $3$ and the square root of $q^2$ is $q$ .
Combine like terms: Combine the like terms outside the radical. $\newline$ $3 \times q \times q$ simplifies to $3q^2$ . $\newline$ So, the final simplified form is $3q^2 \sqrt{2}$ .

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