Square root of 51
√51 ≈ 7.1414. The square root of 51 is about 7.1414. 51 is not a perfect square, so √51 is irrational: its decimals never end or repeat.
| Value | 7.14142843 |
|---|---|
| Rounded | 7.1 (1 dp) · 7.14 (2 dp) · 7.141 (3 dp) |
| Simplest radical form | √51 |
| Perfect square? | No — between 7² = 49 and 8² = 64 |
| 51 squared | 2,601 |
Estimating √51 in your head
Start from the nearest perfect square, 7² = 49. 51 is 2 more than that. Divide the difference by twice the root, 14, and add it:
√51 ≈ 7 + 2 ÷ 14 ≈ 7.143
The true value is 7.1414, so the one-step estimate is off by about 0.001. The estimate always comes out slightly high, and it is closest when 51 is near a perfect square. The method is explained in estimating square roots in your head.
Can √51 be simplified?
No. 51 has no perfect-square factor besides 1, so √51 is already in simplest radical form.
Frequently asked questions
What is the square root of 51?
The square root of 51 is about 7.1414. 51 is not a perfect square, so √51 is irrational: its decimals never end or repeat.
Is 51 a perfect square?
No. It lies between 7² = 49 and 8² = 64.
What is √51 in simplest radical form?
√51 is already in simplest form: 51 has no square factor other than 1.
Practise estimating square rootsNearby: √50 · √52 · all square roots to 150