Square root of 57
√57 ≈ 7.5498. The square root of 57 is about 7.5498. 57 is not a perfect square, so √57 is irrational: its decimals never end or repeat.
| Value | 7.54983444 |
|---|---|
| Rounded | 7.5 (1 dp) · 7.55 (2 dp) · 7.550 (3 dp) |
| Simplest radical form | √57 |
| Perfect square? | No — between 7² = 49 and 8² = 64 |
| 57 squared | 3,249 |
Estimating √57 in your head
Start from the nearest perfect square, 8² = 64. 57 is 7 less than that. Divide the difference by twice the root, 16, and subtract it:
√57 ≈ 8 − 7 ÷ 16 ≈ 7.563
The true value is 7.5498, so the one-step estimate is off by about 0.013. The estimate always comes out slightly high, and it is closest when 57 is near a perfect square. The method is explained in estimating square roots in your head.
Can √57 be simplified?
No. 57 has no perfect-square factor besides 1, so √57 is already in simplest radical form.
Frequently asked questions
What is the square root of 57?
The square root of 57 is about 7.5498. 57 is not a perfect square, so √57 is irrational: its decimals never end or repeat.
Is 57 a perfect square?
No. It lies between 7² = 49 and 8² = 64.
What is √57 in simplest radical form?
√57 is already in simplest form: 57 has no square factor other than 1.
Practise estimating square rootsNearby: √56 · √58 · all square roots to 150