Square root of 135
√135 ≈ 11.619. The square root of 135 is about 11.619, which simplifies to 3√15. 135 is not a perfect square, so √135 is irrational: its decimals never end or repeat.
| Value | 11.61895004 |
|---|---|
| Rounded | 11.6 (1 dp) · 11.62 (2 dp) · 11.619 (3 dp) |
| Simplest radical form | 3√15 |
| Perfect square? | No — between 11² = 121 and 12² = 144 |
| 135 squared | 18,225 |
Estimating √135 in your head
Start from the nearest perfect square, 12² = 144. 135 is 9 less than that. Divide the difference by twice the root, 24, and subtract it:
√135 ≈ 12 − 9 ÷ 24 ≈ 11.625
The true value is 11.619, so the one-step estimate is off by about 0.006. The estimate always comes out slightly high, and it is closest when 135 is near a perfect square. The method is explained in estimating square roots in your head.
Simplifying √135
Find the largest perfect square that divides 135: it is 9, since 135 = 9 × 15. Take its root outside: √135 = √9 × √15 = 3√15.
Frequently asked questions
What is the square root of 135?
The square root of 135 is about 11.619, which simplifies to 3√15. 135 is not a perfect square, so √135 is irrational: its decimals never end or repeat.
Is 135 a perfect square?
No. It lies between 11² = 121 and 12² = 144.
What is √135 in simplest radical form?
√135 = √(9 × 15) = 3√15.
Practise estimating square rootsNearby: √134 · √136 · all square roots to 150