Square root of 134
√134 ≈ 11.5758. The square root of 134 is about 11.5758. 134 is not a perfect square, so √134 is irrational: its decimals never end or repeat.
| Value | 11.5758369 |
|---|---|
| Rounded | 11.6 (1 dp) · 11.58 (2 dp) · 11.576 (3 dp) |
| Simplest radical form | √134 |
| Perfect square? | No — between 11² = 121 and 12² = 144 |
| 134 squared | 17,956 |
Estimating √134 in your head
Start from the nearest perfect square, 12² = 144. 134 is 10 less than that. Divide the difference by twice the root, 24, and subtract it:
√134 ≈ 12 − 10 ÷ 24 ≈ 11.583
The true value is 11.5758, so the one-step estimate is off by about 0.007. The estimate always comes out slightly high, and it is closest when 134 is near a perfect square. The method is explained in estimating square roots in your head.
Can √134 be simplified?
No. 134 has no perfect-square factor besides 1, so √134 is already in simplest radical form.
Frequently asked questions
What is the square root of 134?
The square root of 134 is about 11.5758. 134 is not a perfect square, so √134 is irrational: its decimals never end or repeat.
Is 134 a perfect square?
No. It lies between 11² = 121 and 12² = 144.
What is √134 in simplest radical form?
√134 is already in simplest form: 134 has no square factor other than 1.
Practise estimating square rootsNearby: √133 · √135 · all square roots to 150