Question

simplify the radical expression.

1. $(sqrt{363})(sqrt{300})$

Explanation:

Step1: Factor radicands into squares

$\sqrt{363} = \sqrt{121 \times 3}$, $\sqrt{300} = \sqrt{100 \times 3}$

Step2: Simplify individual radicals

$\sqrt{121 \times 3} = 11\sqrt{3}$, $\sqrt{100 \times 3} = 10\sqrt{3}$

Step3: Multiply simplified radicals

$(11\sqrt{3})(10\sqrt{3}) = 11 \times 10 \times (\sqrt{3})^2$

Step4: Compute final value

$110 \times 3 = 330$

Answer:

330