Square root of 34
√34 ≈ 5.831. The square root of 34 is about 5.831. 34 is not a perfect square, so √34 is irrational: its decimals never end or repeat.
| Value | 5.83095189 |
|---|---|
| Rounded | 5.8 (1 dp) · 5.83 (2 dp) · 5.831 (3 dp) |
| Simplest radical form | √34 |
| Perfect square? | No — between 5² = 25 and 6² = 36 |
| 34 squared | 1,156 |
Estimating √34 in your head
Start from the nearest perfect square, 6² = 36. 34 is 2 less than that. Divide the difference by twice the root, 12, and subtract it:
√34 ≈ 6 − 2 ÷ 12 ≈ 5.833
The true value is 5.831, so the one-step estimate is off by about 0.002. The estimate always comes out slightly high, and it is closest when 34 is near a perfect square. The method is explained in estimating square roots in your head.
Can √34 be simplified?
No. 34 has no perfect-square factor besides 1, so √34 is already in simplest radical form.
Frequently asked questions
What is the square root of 34?
The square root of 34 is about 5.831. 34 is not a perfect square, so √34 is irrational: its decimals never end or repeat.
Is 34 a perfect square?
No. It lies between 5² = 25 and 6² = 36.
What is √34 in simplest radical form?
√34 is already in simplest form: 34 has no square factor other than 1.
Practise estimating square rootsNearby: √33 · √35 · all square roots to 150