How to Simplify Square Roots (Radicals) in 3 Steps
Published 15 November 2026 · Math
Try it nowSquare Root Calculator →Simplifying a square root means writing it so no perfect square is left under the √ sign. Teachers and exam boards expect answers like 6√2 rather than √72. Our square root calculator does it instantly, but here is how to do it by hand.
Step 1: Know your perfect squares
4, 9, 16, 25, 36, 49, 64, 81, 100, 121, 144…
Step 2: Find the largest perfect square factor
For √72, the factors include 4, 9 and 36. The largest perfect square is 36, so 72 = 36 × 2.
Step 3: Split and take the root
Worked examples
| Root | Split | Simplified |
|---|---|---|
| √50 | 25 × 2 | 5√2 |
| √48 | 16 × 3 | 4√3 |
| √200 | 100 × 2 | 10√2 |
| √180 | 36 × 5 | 6√5 |
| √45 | 9 × 5 | 3√5 |
Estimating a square root
Find the perfect squares either side. √40 lies between √36 = 6 and √49 = 7, closer to 6, so about 6.3 (the exact value is 6.3246).
Can you add square roots?
Only like terms: 3√2 + 5√2 = 8√2, but √2 + √3 cannot be combined. Simplify first – √8 + √18 = 2√2 + 3√2 = 5√2.
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15 Nov 2026