Introduction
Simplify the square root of 48 by breaking it down into its prime factors, resulting in the clean expression 4√3; this guide walks you through each step, explains the underlying math, and answers common questions, making the process clear and accessible for learners of all levels.
Understanding how to simplify radicals is a foundational skill in algebra and geometry, and mastering the technique for √48 builds confidence for tackling more complex expressions such as √75 or √120. By the end of this article you will know exactly how to reduce any square root to its simplest radical form, and you will have a toolbox of strategies you can apply repeatedly.
Basically where a lot of people lose the thread.
Steps
Step 1: Identify the radicand and search for perfect square factors
The number inside the radical is called the radicand. For √48, the radicand is 48. Begin by listing the prime factors of 48:
- 48 ÷ 2 = 24
- 24 ÷ 2 = 12
- 12 ÷ 2 = 6
- 6 ÷ 2 = 3
- 3 ÷ 3 = 1
Thus, 48 = 2⁴ × 3. Notice that 2⁴ contains the perfect square 2² (which equals
