The surd form of $\sqrt{45}$ is $3\sqrt{5}$.

To understand why $\sqrt{45}$ can be expressed as $3\sqrt{5}$, we first need to factor the number $45$ into its prime components. The number $45$ can be expressed as the product of $9$ and $5$, since $9 \times 5 = 45$. Further, we can break down $9$ into $3 \times 3$. Thus, the prime factorization of $45$ is given by:

When we take the square root of $45$, we can rewrite it as the square root of the product of its prime factors:

Using the property of square roots, which states that $\sqrt{a \times b} = \sqrt{a} \times \sqrt{b}$, we can separate the factors under the square root:

Since $\sqrt{3 \times 3}$ simplifies to $3$, we can further simplify the expression to:

In GCSE Maths, simplifying surds is a crucial skill. A surd is defined as an irrational number that cannot be simplified to eliminate the square root (or cube root, etc.). In this instance, $\sqrt{5}$ remains a surd because it cannot be further simplified into a rational number. By expressing $\sqrt{45}$ as $3\sqrt{5}$, we have simplified the surd to its most fundamental form, making it more manageable for subsequent calculations.