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Simplify. Assume $s$ is greater than or equal to zero. $\newline$ $\sqrt{45s^3}$

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Simplify radical expressions with variables

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Q. Simplify. Assume

s

is greater than or equal to zero.

\newline

\sqrt{45s^3}

Factorize $45s^3$ : Factorize $45s^3$ to find perfect squares. $\newline$ The prime factorization of $45$ is $3 \times 3 \times 5$ , and $s^3$ can be written as $s^2 \times s$ . Therefore, $45s^3$ can be factorized as: $\newline$ $45s^3 = 3 \times 3 \times 5 \times s^2 \times s$
Group Perfect Squares: Group the factors into perfect squares. $\newline$ We can group the factors into perfect squares as follows: $\newline$ $45s^3 = (3^2) \cdot (s^2) \cdot 5 \cdot s$
Simplify Square Root: Simplify the square root of the expression. $\newline$ Now we take the square root of the expression, keeping in mind that the square root of a perfect square is just the base of the square: $\newline$ $\sqrt{45s^3} = \sqrt{(3^2) \cdot (s^2) \cdot 5 \cdot s}$ $\newline$ $= 3 \cdot s \cdot \sqrt{5s}$

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