Question

simplify the radical expression.

1. $(sqrt{18})(sqrt{72})$

Explanation:

Step1: Factor radicands into squares

$\sqrt{18} = \sqrt{9 \times 2}$, $\sqrt{72} = \sqrt{36 \times 2}$

Step2: Simplify individual radicals

$\sqrt{9 \times 2} = 3\sqrt{2}$, $\sqrt{36 \times 2} = 6\sqrt{2}$

Step3: Multiply simplified radicals

$(3\sqrt{2})(6\sqrt{2}) = 3 \times 6 \times \sqrt{2} \times \sqrt{2}$

Step4: Compute the product

$18 \times 2 = 36$

Answer:

36