Square root of 69
√69 ≈ 8.3066. The square root of 69 is about 8.3066. 69 is not a perfect square, so √69 is irrational: its decimals never end or repeat.
| Value | 8.30662386 |
|---|---|
| Rounded | 8.3 (1 dp) · 8.31 (2 dp) · 8.307 (3 dp) |
| Simplest radical form | √69 |
| Perfect square? | No — between 8² = 64 and 9² = 81 |
| 69 squared | 4,761 |
Estimating √69 in your head
Start from the nearest perfect square, 8² = 64. 69 is 5 more than that. Divide the difference by twice the root, 16, and add it:
√69 ≈ 8 + 5 ÷ 16 ≈ 8.313
The true value is 8.3066, so the one-step estimate is off by about 0.006. The estimate always comes out slightly high, and it is closest when 69 is near a perfect square. The method is explained in estimating square roots in your head.
Can √69 be simplified?
No. 69 has no perfect-square factor besides 1, so √69 is already in simplest radical form.
Frequently asked questions
What is the square root of 69?
The square root of 69 is about 8.3066. 69 is not a perfect square, so √69 is irrational: its decimals never end or repeat.
Is 69 a perfect square?
No. It lies between 8² = 64 and 9² = 81.
What is √69 in simplest radical form?
√69 is already in simplest form: 69 has no square factor other than 1.
Practise estimating square rootsNearby: √68 · √70 · all square roots to 150