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Perform the multiplication and express the result in the simplest form. $\newline$ $\sqrt{12}\times\sqrt{4}$

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Multiply radical expressions

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Q. Perform the multiplication and express the result in the simplest form.

\newline

\sqrt{12}\times\sqrt{4}

Apply product rule of radicals: We have: $\sqrt{12} \times \sqrt{4}$ Apply the product rule of radicals. $\sqrt{12} \times \sqrt{4} = \sqrt{12 \times 4}$
Multiply inside the radical: Now, let's multiply inside the radical. $\sqrt{12 \times 4} = \sqrt{48}$
Simplify by factoring: But wait, $48$ can be simplified cuz it's $16$ times $3$ , and $16$ is a perfect square. $\newline$ So, we can write $\sqrt{48}$ as $\sqrt{16 \times 3}$
Take square root out: Now, we can take the square root of $16$ out of the radical, since it's a perfect square. $\newline$ $\sqrt{16 \times 3} = \sqrt{16} \times \sqrt{3}$
Final simplified form: And we know that $\sqrt{16}$ is $4$ , so we have: $4 \times \sqrt{3}$
Final simplified form: And we know that $\sqrt{16}$ is $4$ , so we have: $\newline$ $4 \times \sqrt{3}$ So, the simplest form of $\sqrt{12} \times \sqrt{4}$ is: $\newline$ $4 \times \sqrt{3}$

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