Simplify the following expression: \$(\sqrt8 \times \sqrt2) \times (3\sqrt5 \times \sqrt10)\$.

To simplify the expression:

\$(\sqrt8 \times \sqrt2) \times (3\sqrt5 \times \sqrt10)\$

Simplify inside the parentheses:

\$\sqrt(8) \times \sqrt(2) = \sqrt(8 \times 2) = \sqrt(16) = 4\$

Simplify the second part inside the parentheses:

\$3\sqrt(5) \times \sqrt(10) = 3 \times \sqrt(5 \times 10) = 3 \times \sqrt(50)\$

\$3 \times \sqrt(25 \times 2) = 3 \times 5\sqrt(2) = 15\sqrt(2)\$

Combine the results:

\$4 \times15\sqrt(2)\$

Multiply the constants:

\$4 \times 15 = 60\$

Therefore, the simplified expression is \$60\sqrt(2)\$.

This option matches our simplified expression \$60\sqrt(2)\$

\$60\sqrt(2)\$

This option is incorrect, as it suggests a different coefficient (50 instead of 60)

\$50\sqrt(2)\$

This option is not correct, as it involves \$\sqrt(3)\$ instead of \$\sqrt(2)\$

\$-50\sqrt(3)\$

This option is not correct, as it does not match our simplified expression \$60\sqrt(2)\$

\$3\sqrt(10)\$

Option

A

Can you summarize what you’ve understood in the above steps?