# Simplify square root 48.

#### Understand the Problem

The question is asking to simplify the square root of 48. This means we need to factor 48 into its prime components and identify perfect squares to reduce the square root expression to its simplest form.

$4\sqrt{3}$

The final answer is $4\sqrt{3}$

#### Steps to Solve

1. Factorize the number inside the square root

First, we need to factorize 48 into its prime factors.

$$48 = 2 \times 24 = 2 \times 2 \times 12 = 2 \times 2 \times 2 \times 6 = 2 \times 2 \times 2 \times 2 \times 3$$

1. Identify perfect square factors

Next, we identify the perfect square factors within the prime factorization of 48. In this case, $$2 \times 2 \times 2 \times 2 = 16$$, which is a perfect square ($(4^2)$), and we're left with 3.

$$48 = 16 \times 3$$

1. Apply the square root to the perfect square factor

Take the square root of the perfect square (16) and leave the remaining factor (3) inside the square root.

$$\sqrt{48} = \sqrt{16 \times 3} = \sqrt{16} \times \sqrt{3} = 4\sqrt{3}$$

The final answer is $4\sqrt{3}$