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Simplify.
Multiply and remove all perfect squares from inside the square roots. Assume
b is positive.

2sqrt(8b^(3))*9sqrt(18 b)=

Simplify. $\newline$ Multiply and remove all perfect squares from inside the square roots. Assume $\newline$ $b$ is positive. $\newline$ $2\sqrt{8b^{3}} \cdot 9\sqrt{18b} =$

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Simplify radical expressions with variables

Full solution

Q. Simplify.

\newline

Multiply and remove all perfect squares from inside the square roots. Assume

\newline

b

is positive.

\newline

2\sqrt{8b^{3}} \cdot 9\sqrt{18b} =

Factor the numbers: Factor the numbers inside the square roots to reveal any perfect squares. $\newline$ We have $2\sqrt{8b^3} \times 9\sqrt{18b}$ . Let's factor $8$ and $18$ to find perfect squares. $\newline$ $8 = 2^3$ and $18 = 2 \times 3^2$ . $\newline$ So, $8b^3 = 2^3 \times b^3$ and $18b = 2 \times 3^2 \times b$ .
Rewrite the expression: Rewrite the expression using the factors found. $\newline$ Now we can rewrite the expression as: $\newline$ $2\sqrt{2^3 \cdot b^3} \cdot 9\sqrt{2 \cdot 3^2 \cdot b}$ .
Simplify the square roots: Simplify the square roots by taking out the perfect squares. $\newline$ We can take the square root of any perfect squares inside the square roots: $\newline$ $2\sqrt{2^2 \cdot 2 \cdot b^2 \cdot b}$ $\cdot 9\sqrt{2 \cdot 3^2 \cdot b}$ $\newline$ = $2 \cdot 2 \cdot b \cdot \sqrt{2b}$ $\cdot 9 \cdot 3 \cdot \sqrt{b}$ $\newline$ = $4b \cdot \sqrt{2b}$ $\cdot 27 \cdot \sqrt{b}$ .
Combine the constants and square roots: Combine the constants and the square roots. $\newline$ Now we multiply the constants together and the square roots together: $\newline$ $(4b \times 27) \times (\sqrt{2b} \times \sqrt{b})$ $\newline$ $= 108b \times \sqrt{2b^2}$ $\newline$ $= 108b \times \sqrt{2 \times b^2}$ .
Simplify the square root: Simplify the square root by taking out the perfect square $b^2$ . $\newline$ Since $b^2$ is a perfect square, we can take $b$ out of the square root: $\newline$ $108b \cdot b \cdot \sqrt{2}$ $\newline$ = $108b^2 \cdot \sqrt{2}$ .

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