Section A: Rules Surd Rules 1. Multiplication Rule: $$ \sqrt{a} \times \sqrt{b}=\sqrt{a \times b} $$ 2. Division Rule: $$ \frac{\sqrt{a}}{\sqrt{b}}=\sqrt{\frac{a}{b}} $$ 3. Addition and Subtraction: Surds can only be added or subtracted if they have the same radicand: $$ 3 \sqrt{2}+4 \sqrt{2}=7 \sqrt{2} $$ 4. Simplifying Surds: $$ \sqrt{a b}=\sqrt{a} \times \sqrt{b} $$ always written in the simplest form where possible. 5. Rationalizing the Denominator: Multiply the numerator and denominator by a suitable surd to remove the square root from thedenominator. The following surds rules will help in simplifying surds and other mathematical expressions: Simplifving Surds: Example: Simplify $$ \sqrt{200} $$ Steps: 1. Factorize 200 into a perfect square and another factor(Prime number): $$ \sqrt{200}=\sqrt{100 \times 2} $$ 2. Split the square root: $$ \sqrt{100} \times \sqrt{2}=10 \sqrt{2} $$ 3. Final answer: $$ 10 \sqrt{2} $$

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Let's apply the surd rules to simplify the expression $$ \sqrt{200} $$ step by step, as outlined in the example provided.

### Step 1: Factorization
We start by factorizing $$ 200 $$ into a perfect square and another factor. The perfect square that divides $$ 200 $$ is $$ 100 $$, which is $$ 10^2 $$. Thus, we can express $$ 200 $$ as:
$$
200 = 100 \times 2
$$

### Step 2: Splitting the Square Root
Using the multiplication rule for surds, we can split the square root:
$$
\sqrt{200} = \sqrt{100 \times 2} = \sqrt{100} \times \sqrt{2}
$$

### Step 3: Simplifying the Square Root
Now, we simplify $$ \sqrt{100} $$:
$$
\sqrt{100} = 10
$$
So, substituting this back into our expression gives:
$$
\sqrt{200} = 10 \times \sqrt{2}
$$

### Final Answer
Thus, the simplified form of $$ \sqrt{200} $$ is:
$$
10 \sqrt{2}
$$

This process demonstrates the application of the surd rules effectively, leading us to the final simplified expression.
To simplify $$ \sqrt{200} $$, factorize 200 into $$ 100 \times 2 $$, then split the square root: $$ \sqrt{100} \times \sqrt{2} = 10 \times \sqrt{2} $$. So, $$ \sqrt{200} = 10 \sqrt{2} $$.

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