Square root of 67
√67 ≈ 8.1854. The square root of 67 is about 8.1854. 67 is not a perfect square, so √67 is irrational: its decimals never end or repeat.
| Value | 8.18535277 |
|---|---|
| Rounded | 8.2 (1 dp) · 8.19 (2 dp) · 8.185 (3 dp) |
| Simplest radical form | √67 |
| Perfect square? | No — between 8² = 64 and 9² = 81 |
| 67 squared | 4,489 |
Estimating √67 in your head
Start from the nearest perfect square, 8² = 64. 67 is 3 more than that. Divide the difference by twice the root, 16, and add it:
√67 ≈ 8 + 3 ÷ 16 ≈ 8.188
The true value is 8.1854, so the one-step estimate is off by about 0.002. The estimate always comes out slightly high, and it is closest when 67 is near a perfect square. The method is explained in estimating square roots in your head.
Can √67 be simplified?
No. 67 has no perfect-square factor besides 1, so √67 is already in simplest radical form.
Frequently asked questions
What is the square root of 67?
The square root of 67 is about 8.1854. 67 is not a perfect square, so √67 is irrational: its decimals never end or repeat.
Is 67 a perfect square?
No. It lies between 8² = 64 and 9² = 81.
What is √67 in simplest radical form?
√67 is already in simplest form: 67 has no square factor other than 1.
Practise estimating square rootsNearby: √66 · √68 · all square roots to 150