How to Simplify Square Root 28- Step-by-Step Guide
How to Simplify √28 in Seconds
Square root of 28. Let's cut to the chase.
The simplified form is 2√7.
That's it. That's the answer. But if you want to understand why—and not just memorize it—keep reading.
The Step-by-Step Process
Step 1: Find the Prime Factorization
Break down 28 into its prime factors.
28 = 4 × 7
Or in prime factors: 28 = 2 × 2 × 7
Step 2: Look for Perfect Squares
A perfect square is a number like 4, 9, 16, 25—anything that can be written as an integer squared.
In 28, you have 2 × 2. That's 2², which equals 4. That's your perfect square.
Step 3: Extract the Square Root
√28 = √(4 × 7)
Split it: √4 × √7
√4 = 2
So: 2 × √7
Result: 2√7
Why This Works
The rule is simple: √(a × b) = √a × √b
When one of those numbers is a perfect square, you can take its square root out of the radical. That's called simplifying the radical.
28 has a perfect square factor: 4. That's why we can simplify it.
Quick Reference Table
| Original | Factorization | Perfect Square | Simplified |
|---|---|---|---|
| √28 | 4 × 7 | 4 | 2√7 |
| √12 | 4 × 3 | 4 | 2√3 |
| √18 | 9 × 2 | 9 | 3√2 |
| √45 | 9 × 5 | 9 | 3√5 |
How to Check Your Answer
Multiply it back out to verify.
2√7 × 2√7 = 4 × 7 = 28 ✓
If you have a calculator handy: √7 ≈ 2.6458
2 × 2.6458 ≈ 5.29
√28 ≈ 5.29 ✓
Common Mistakes
- Forgetting to find the largest perfect square. Yes, 28 = 2 × 14, but 2 isn't a perfect square. You need to keep factoring until you hit one.
- Leaving the radical unsimplified. √28 is technically correct, but it's not simplified. 2√7 is the proper answer.
- Confusing the process with rationalizing denominators. This is a different skill entirely. Don't mix them up.
When You'll Actually Use This
Simplifying radicals shows up in:
- Algebra classes (always)
- Geometry (distance formulas, Pythagorean theorem)
- Calculus (rationalizing expressions)
- Anywhere radicals need to be combined or compared
It's a foundational skill. Master it now, or struggle with it later.