Square root of 27
√27 ≈ 5.1962. The square root of 27 is about 5.1962, which simplifies to 3√3. 27 is not a perfect square, so √27 is irrational: its decimals never end or repeat.
| Value | 5.19615242 |
|---|---|
| Rounded | 5.2 (1 dp) · 5.20 (2 dp) · 5.196 (3 dp) |
| Simplest radical form | 3√3 |
| Perfect square? | No — between 5² = 25 and 6² = 36 |
| 27 squared | 729 |
Estimating √27 in your head
Start from the nearest perfect square, 5² = 25. 27 is 2 more than that. Divide the difference by twice the root, 10, and add it:
√27 ≈ 5 + 2 ÷ 10 ≈ 5.2
The true value is 5.1962, so the one-step estimate is off by about 0.004. The estimate always comes out slightly high, and it is closest when 27 is near a perfect square. The method is explained in estimating square roots in your head.
Simplifying √27
Find the largest perfect square that divides 27: it is 9, since 27 = 9 × 3. Take its root outside: √27 = √9 × √3 = 3√3.
Frequently asked questions
What is the square root of 27?
The square root of 27 is about 5.1962, which simplifies to 3√3. 27 is not a perfect square, so √27 is irrational: its decimals never end or repeat.
Is 27 a perfect square?
No. It lies between 5² = 25 and 6² = 36.
What is √27 in simplest radical form?
√27 = √(9 × 3) = 3√3.
Practise estimating square rootsNearby: √26 · √28 · all square roots to 150