Square root of 33
√33 ≈ 5.7446. The square root of 33 is about 5.7446. 33 is not a perfect square, so √33 is irrational: its decimals never end or repeat.
| Value | 5.74456265 |
|---|---|
| Rounded | 5.7 (1 dp) · 5.74 (2 dp) · 5.745 (3 dp) |
| Simplest radical form | √33 |
| Perfect square? | No — between 5² = 25 and 6² = 36 |
| 33 squared | 1,089 |
Estimating √33 in your head
Start from the nearest perfect square, 6² = 36. 33 is 3 less than that. Divide the difference by twice the root, 12, and subtract it:
√33 ≈ 6 − 3 ÷ 12 ≈ 5.75
The true value is 5.7446, so the one-step estimate is off by about 0.005. The estimate always comes out slightly high, and it is closest when 33 is near a perfect square. The method is explained in estimating square roots in your head.
Can √33 be simplified?
No. 33 has no perfect-square factor besides 1, so √33 is already in simplest radical form.
Frequently asked questions
What is the square root of 33?
The square root of 33 is about 5.7446. 33 is not a perfect square, so √33 is irrational: its decimals never end or repeat.
Is 33 a perfect square?
No. It lies between 5² = 25 and 6² = 36.
What is √33 in simplest radical form?
√33 is already in simplest form: 33 has no square factor other than 1.
Practise estimating square rootsNearby: √32 · √34 · all square roots to 150