Multiply. Write your answer in simplest form. $\newline$ $\sqrt{15} \times \sqrt{2}$ $\newline$ _____________

Full solution

Q. Multiply. Write your answer in simplest form.

\newline

\sqrt{15} \times \sqrt{2}

\newline

_____________

Apply product rule for square roots: Apply the product rule for square roots. $\newline$ The product rule for square roots states that the square root of a product is equal to the product of the square roots. Therefore, we can combine the square roots of $15$ and $2$ into a single square root. $\newline$ $\sqrt{15} \times \sqrt{2} = \sqrt{15 \times 2}$
Multiply numbers inside square root: Multiply the numbers inside the square root. $\newline$ Now we multiply the numbers inside the square root to simplify the expression. $\newline$ $\sqrt{15 \times 2} = \sqrt{30}$
Determine if square root can be simplified further: Determine if the square root can be simplified further. $\newline$ The number $30$ is not a perfect square, and it cannot be broken down into a product of a perfect square and another integer. Therefore, $\sqrt{30}$ is already in its simplest form.