Square root of 28
√28 ≈ 5.2915. The square root of 28 is about 5.2915, which simplifies to 2√7. 28 is not a perfect square, so √28 is irrational: its decimals never end or repeat.
| Value | 5.29150262 |
|---|---|
| Rounded | 5.3 (1 dp) · 5.29 (2 dp) · 5.292 (3 dp) |
| Simplest radical form | 2√7 |
| Perfect square? | No — between 5² = 25 and 6² = 36 |
| 28 squared | 784 |
Estimating √28 in your head
Start from the nearest perfect square, 5² = 25. 28 is 3 more than that. Divide the difference by twice the root, 10, and add it:
√28 ≈ 5 + 3 ÷ 10 ≈ 5.3
The true value is 5.2915, so the one-step estimate is off by about 0.008. The estimate always comes out slightly high, and it is closest when 28 is near a perfect square. The method is explained in estimating square roots in your head.
Simplifying √28
Find the largest perfect square that divides 28: it is 4, since 28 = 4 × 7. Take its root outside: √28 = √4 × √7 = 2√7.
Frequently asked questions
What is the square root of 28?
The square root of 28 is about 5.2915, which simplifies to 2√7. 28 is not a perfect square, so √28 is irrational: its decimals never end or repeat.
Is 28 a perfect square?
No. It lies between 5² = 25 and 6² = 36.
What is √28 in simplest radical form?
√28 = √(4 × 7) = 2√7.
Practise estimating square rootsNearby: √27 · √29 · all square roots to 150