Simplify the surd expressions: (i) (√5√3 - 2√3)(√27 + 3√1)

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Question 54:
This question asks to simplify surd expressions. There are three parts.

• Part (i): Simplify $(\sqrt{5}\sqrt{3} - 2\sqrt{3})(\sqrt{27} + 3\sqrt{1})$

Step 1: Simplify the terms within each parenthesis.

$$\sqrt{5}\sqrt{3} = \sqrt{15}$$ $$\sqrt{27} = \sqrt{9 \times 3} = 3\sqrt{3}$$ $$3\sqrt{1} = 3$$

The expression becomes:

$$$$