Square root of 66
√66 ≈ 8.124. The square root of 66 is about 8.124. 66 is not a perfect square, so √66 is irrational: its decimals never end or repeat.
| Value | 8.1240384 |
|---|---|
| Rounded | 8.1 (1 dp) · 8.12 (2 dp) · 8.124 (3 dp) |
| Simplest radical form | √66 |
| Perfect square? | No — between 8² = 64 and 9² = 81 |
| 66 squared | 4,356 |
Estimating √66 in your head
Start from the nearest perfect square, 8² = 64. 66 is 2 more than that. Divide the difference by twice the root, 16, and add it:
√66 ≈ 8 + 2 ÷ 16 ≈ 8.125
The true value is 8.124, so the one-step estimate is off by less than 0.001. The estimate always comes out slightly high, and it is closest when 66 is near a perfect square. The method is explained in estimating square roots in your head.
Can √66 be simplified?
No. 66 has no perfect-square factor besides 1, so √66 is already in simplest radical form.
Frequently asked questions
What is the square root of 66?
The square root of 66 is about 8.124. 66 is not a perfect square, so √66 is irrational: its decimals never end or repeat.
Is 66 a perfect square?
No. It lies between 8² = 64 and 9² = 81.
What is √66 in simplest radical form?
√66 is already in simplest form: 66 has no square factor other than 1.
Practise estimating square rootsNearby: √65 · √67 · all square roots to 150