4.9) \( 2 \sqrt{6} \times 5 \sqrt{3} \)

To solve \( 2 \sqrt{6} \times 5 \sqrt{3} \), start by multiplying the coefficients (the numbers outside the square roots) and then the square roots themselves. First, multiply the coefficients: \( 2 \times 5 = 10 \). Then, multiply the square roots: \( \sqrt{6} \times \sqrt{3} = \sqrt{18} \). Now, combine the results: \( 10 \times \sqrt{18} \). To simplify \( \sqrt{18} \), recognize that it can be expressed as \( \sqrt{9 \times 2} = 3\sqrt{2} \). Therefore, the final answer is: \( 10 \times 3 \sqrt{2} = 30 \sqrt{2} \). So, the expression \( 2 \sqrt{6} \times 5 \sqrt{3} \) simplifies to \( 30 \sqrt{2} \).