Square root of 133
√133 ≈ 11.5326. The square root of 133 is about 11.5326. 133 is not a perfect square, so √133 is irrational: its decimals never end or repeat.
| Value | 11.53256259 |
|---|---|
| Rounded | 11.5 (1 dp) · 11.53 (2 dp) · 11.533 (3 dp) |
| Simplest radical form | √133 |
| Perfect square? | No — between 11² = 121 and 12² = 144 |
| 133 squared | 17,689 |
Estimating √133 in your head
Start from the nearest perfect square, 12² = 144. 133 is 11 less than that. Divide the difference by twice the root, 24, and subtract it:
√133 ≈ 12 − 11 ÷ 24 ≈ 11.542
The true value is 11.5326, so the one-step estimate is off by about 0.009. The estimate always comes out slightly high, and it is closest when 133 is near a perfect square. The method is explained in estimating square roots in your head.
Can √133 be simplified?
No. 133 has no perfect-square factor besides 1, so √133 is already in simplest radical form.
Frequently asked questions
What is the square root of 133?
The square root of 133 is about 11.5326. 133 is not a perfect square, so √133 is irrational: its decimals never end or repeat.
Is 133 a perfect square?
No. It lies between 11² = 121 and 12² = 144.
What is √133 in simplest radical form?
√133 is already in simplest form: 133 has no square factor other than 1.
Practise estimating square rootsNearby: √132 · √134 · all square roots to 150