Square root of 20
√20 ≈ 4.4721. The square root of 20 is about 4.4721, which simplifies to 2√5. 20 is not a perfect square, so √20 is irrational: its decimals never end or repeat.
| Value | 4.47213595 |
|---|---|
| Rounded | 4.5 (1 dp) · 4.47 (2 dp) · 4.472 (3 dp) |
| Simplest radical form | 2√5 |
| Perfect square? | No — between 4² = 16 and 5² = 25 |
| 20 squared | 400 |
Estimating √20 in your head
Start from the nearest perfect square, 4² = 16. 20 is 4 more than that. Divide the difference by twice the root, 8, and add it:
√20 ≈ 4 + 4 ÷ 8 ≈ 4.5
The true value is 4.4721, so the one-step estimate is off by about 0.028. The estimate always comes out slightly high, and it is closest when 20 is near a perfect square. The method is explained in estimating square roots in your head.
Simplifying √20
Find the largest perfect square that divides 20: it is 4, since 20 = 4 × 5. Take its root outside: √20 = √4 × √5 = 2√5.
Frequently asked questions
What is the square root of 20?
The square root of 20 is about 4.4721, which simplifies to 2√5. 20 is not a perfect square, so √20 is irrational: its decimals never end or repeat.
Is 20 a perfect square?
No. It lies between 4² = 16 and 5² = 25.
What is √20 in simplest radical form?
√20 = √(4 × 5) = 2√5.
Practise estimating square rootsNearby: √19 · √21 · all square roots to 150