1. **Problem Statement:** We need to determine whether the given expressions are surds by simplifying them fully. 2. **Definition:** A surd is an irrational root that cannot be simplified to remove the root. 3. **Part (a): Simplify $2\sqrt{144}$** - Calculate $\sqrt{144}$: since $144 = 12^2$, $\sqrt{144} = 12$. - Multiply by 2: $2 \times 12 = 24$. - Since $24$ is a rational number (no root remains), $2\sqrt{144}$ is **not** a surd. 4. **Part (b): Simplify $5\sqrt{60}$** - Factorize 60: $60 = 4 \times 15$. - Simplify the root: $\sqrt{60} = \sqrt{4 \times 15} = \sqrt{4} \times \sqrt{15} = 2\sqrt{15}$. - Multiply by 5: $5 \times 2\sqrt{15} = 10\sqrt{15}$. - Since $\sqrt{15}$ cannot be simplified further and is irrational, $5\sqrt{60}$ **is** a surd. 5. **Part (c): Simplify $3\sqrt{324}$** - Calculate $\sqrt{324}$: since $324 = 18^2$, $\sqrt{324} = 18$. - Multiply by 3: $3 \times 18 = 54$. - Since $54$ is rational, $3\sqrt{324}$ is **not** a surd. **Final answers:** - (a) Not a surd - (b) Is a surd - (c) Not a surd