Square root of 65
√65 ≈ 8.0623. The square root of 65 is about 8.0623. 65 is not a perfect square, so √65 is irrational: its decimals never end or repeat.
| Value | 8.06225775 |
|---|---|
| Rounded | 8.1 (1 dp) · 8.06 (2 dp) · 8.062 (3 dp) |
| Simplest radical form | √65 |
| Perfect square? | No — between 8² = 64 and 9² = 81 |
| 65 squared | 4,225 |
Estimating √65 in your head
Start from the nearest perfect square, 8² = 64. 65 is 1 more than that. Divide the difference by twice the root, 16, and add it:
√65 ≈ 8 + 1 ÷ 16 ≈ 8.063
The true value is 8.0623, so the one-step estimate is off by less than 0.001. The estimate always comes out slightly high, and it is closest when 65 is near a perfect square. The method is explained in estimating square roots in your head.
Can √65 be simplified?
No. 65 has no perfect-square factor besides 1, so √65 is already in simplest radical form.
Frequently asked questions
What is the square root of 65?
The square root of 65 is about 8.0623. 65 is not a perfect square, so √65 is irrational: its decimals never end or repeat.
Is 65 a perfect square?
No. It lies between 8² = 64 and 9² = 81.
What is √65 in simplest radical form?
√65 is already in simplest form: 65 has no square factor other than 1.
Practise estimating square rootsNearby: √64 · √66 · all square roots to 150