Square root of 52
√52 ≈ 7.2111. The square root of 52 is about 7.2111, which simplifies to 2√13. 52 is not a perfect square, so √52 is irrational: its decimals never end or repeat.
| Value | 7.21110255 |
|---|---|
| Rounded | 7.2 (1 dp) · 7.21 (2 dp) · 7.211 (3 dp) |
| Simplest radical form | 2√13 |
| Perfect square? | No — between 7² = 49 and 8² = 64 |
| 52 squared | 2,704 |
Estimating √52 in your head
Start from the nearest perfect square, 7² = 49. 52 is 3 more than that. Divide the difference by twice the root, 14, and add it:
√52 ≈ 7 + 3 ÷ 14 ≈ 7.214
The true value is 7.2111, so the one-step estimate is off by about 0.003. The estimate always comes out slightly high, and it is closest when 52 is near a perfect square. The method is explained in estimating square roots in your head.
Simplifying √52
Find the largest perfect square that divides 52: it is 4, since 52 = 4 × 13. Take its root outside: √52 = √4 × √13 = 2√13.
Frequently asked questions
What is the square root of 52?
The square root of 52 is about 7.2111, which simplifies to 2√13. 52 is not a perfect square, so √52 is irrational: its decimals never end or repeat.
Is 52 a perfect square?
No. It lies between 7² = 49 and 8² = 64.
What is √52 in simplest radical form?
√52 = √(4 × 13) = 2√13.
Practise estimating square rootsNearby: √51 · √53 · all square roots to 150